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• Abbes, A. and Bouche, T.: Théorème de Hilbert-Samuel “arithmétique”, Ann. Inst. Fourier 45\br(1995)\brr375–401
• Abramovich, D. and Voloch, J. F.: Lang’s conjectures, fibered powers, and uniformity, New York J. Math. 2\br(1996)\brr20–34
• Albert, A.: Structure of Algebras, Revised Printing, Amer. Math. Soc. Coll. Pub., Vol. XXIV, Amer. Math. Soc., Providence, R.I. 1961
• Software Optimization Guide for AMD Athlon$^\textrm {TM}$ 64 and AMD Opteron$^\textrm {TM}$ Processors, Rev. 3.04, AMD, Sunnyvale (CA) 2004
• Amitsur, S. A.: Generic splitting fields of central simple algebras, Annals of Math. 62\br(1955)\brr8–43
• Amitsur, S. A.: On central division algebras, Israel J. Math. 12\br(1972)\brr408–420
• Amitsur, S. A.: Generic splitting fields, in: van Oystaeyen, F. and Verschoren, A. (Eds.): Brauer groups in ring theory and algebraic geometry, Proceedings of a conference held at Antwerp 1981, Lecture Notes Math. 917, Springer, Berlin, Heidelberg, New York 1982, 1–24
• Apéry, F.: Models of the real projective plane, Vieweg, Braunschweig 1987
• Apostol, T. M.: Introduction to analytic number theory, Springer, New York-Heidelberg 1976
• \textcyr{Arakelov, S. Yu.: Teoriya peresecheniĭ divizorov na arifmeticheskoĭ poverkhnosti, Izv. Akad. Nauk SSSR, Ser. Mat. 38\br(1974)\brr1179–1192,} English translation: Arakelov, S. Yu.: Intersection theory of divisors on an arithmetic surface, Math. USSR Izv. 8\br(1974)\brr1167–1180
• Artin, E.: Über einen Satz von J. H. Maclagan-Wedderburn, Abh. Math. Sem. Univ. Hamburg 5\br(1927)\brr245–250
• Artin, E.: Zur Theorie der hyperkomplexen Zahlen, Abh. Math. Sem. Univ. Hamburg 5\br(1927)\brr251–260
• Artin, E., Nesbitt, C. J., and Thrall, R.: Rings with minimum condition, Univ. of Michigan Press, Ann Arbor 1948
• Artin, M.: Left Ideals in Maximal Orders, in: van Oystaeyen, F. and Verschoren, A. (Eds.): Brauer groups in ring theory and algebraic geometry, Proceedings of a conference held at Antwerp 1981, Lecture Notes Math. 917, Springer, Berlin, Heidelberg, New York 1982, 182–193
• Artin, M. (Notes by Verschoren, A.): Brauer-Severi varieties, in: van Oystaeyen, F. and Verschoren, A. (Eds.): Brauer groups in ring theory and algebraic geometry, Proceedings of a conference held at Antwerp 1981, Lecture Notes Math. 917, Springer, Berlin, Heidelberg, New York 1982, 194–210
• Artin, M. and Mumford, D.: Some elementary examples of unirational varieties which are not rational, Proc. London Math. Soc. 25\br(1972)\brr75–95
• Atiyah, M. F. and Wall, C. T. C.: Cohomomology of groups, in: Algebraic number theory, Edited by J. W. S. Cassels and A. Fröhlich, Academic Press and Thompson Book Co., London and Washington 1967
• Auslander, M. and Goldman, O.: The Brauer group of a commutative ring, Trans. Amer. Math. Soc. 97\br(1960)\brr367–409
• Azumaya, G.: On maximally central algebras, Nagoya Math. J. 2\br(1951)\brr119–150
• Barth, W., Hulek, K., Peters, C., and Van de Ven, A.: Compact complex surfaces, Second edition, Springer, Berlin 2004
• Batyrev, V. V. and Manin, Yu. I.: Sur le nombre des points rationnels de hauteur borné des variétés algébriques, Math. Ann. 286\br(1990)\brr27–43
• Batyrev, V. V. and Tschinkel, Y.: Rational points on some Fano cubic bundles, C. R. Acad. Sci. Paris 323\br(1996)\brr41–46
• Batyrev, V. V. and Tschinkel, Y.: Manin’s conjecture for toric varieties, J. Algebraic Geom. 7\br(1998)\brr15–53
• Beauville, A.: Complex algebraic surfaces, LMS Lecture Note Series 68, Cambridge University Press, Cambridge 1983
• Beck, M., Pine, E., Tarrant, W., and Yarbrough Jensen, K.: New integer representations as the sum of three cubes, Math. Comp. 76\br(2007)\brr1683–1690
• van den Bergh, M.: The Brauer-Severi scheme of the trace ring of generic matrices, in: Perspectives in ring theory (Antwerp 1987), NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 233, Kluwer Acad. Publ., Dordrecht 1988, 333–338
• Bernstein, D. J.: Enumerating solutions to $p(a)+q(b)=r(c)+s(d)$, Math. Comp. 70\br(2001)\brr389–394
• Bernstein, D. J.: threecubes, Web page available at the URL: http://\discretionary{}cr.yp.to/\discretionary{}threecubes.html
• Bertuccioni, I.: Brauer groups and cohomology, Arch. Math. 84\br(2005)\brr406–411
• Białynicki-Birula, A.: A note on deformations of Severi-Brauer varieties and relatively minimal models of fields of genus $0$, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 18\br(1970)\brr175–176
• \textcyr{Belotserkovski, Yu. F. [Bilu, Yu.]: Ravnomernoe raspredelenie algebraicheskikh chisel blizkikh k edinichnomu krugu, Vestsi1 Akad. Navuk BSSR, Ser. Fi1z.-Mat. Navuk 1988\br(1988)\brr49-52, 124}
• Bhowmik, G., Essouabri, D. and Lichtin, B.: Meromorphic continuation of multivariable Euler products, Forum Math. 19\br(2007)\brr1111–1139
• Bilu, Yu.: Limit distribution of small points on algebraic tori, Duke Math. J. 89\br(1997)\brr465-476
• Billard, H.: Propriétés arithmétiques d’une famille de surfaces $K3$, Compositio Math. 108\br(1997)\brr247–275
• Birch, B. J.: Forms in many variables, Proc. Roy. Soc. Ser. A 265\br(1961/1962)\brr245–263
• Blanchard, A.: Les corps non commutatifs, Presses Univ. de France, Vendôme 1972
• Blanchet, A.: Function fields of generalized Brauer-Severi varieties, Comm. in Algebra 19\br(1991)\brr97–118
• Blomer, V., Brüdern, J., and Salberger, P.: On a senary cubic form, arXiv:1205.0190
• Bogomolov, F. and Tschinkel, Y.: Rational curves and points on $K3$ surfaces, Amer. J. Math. 127\br(2005)\brr825–835
• Bombieri, E.: Problems and results on the distribution of algebraic points on algebraic varieites, Journal de Théorie des Nombres de Bordeaux 21\br(2009)\brr41–57
• \textcyr{Borevich, Z. I. i Shafarevich, I. R.: Teoriya chisel, Tretp1e izdanie, Nauka, Moskva 1985} English translation: Borevich, Z. I. and Shafarevich, I. R.: Number theory, Academic Press, New York-London 1966
• Bost, J.-B., Gillet, H., Soulé, C.: Heights of projective varieties and positive Green forms, J. Amer. Math. Soc. 7\br(1994)\brr903-1027
• Bott, R.: On a theorem of Lefschetz, Michigan Math. J. 6\br(1959)\brr211–216
• Bourbaki, N.: Éléments de Mathématique, Livre III: Topologie générale, Chapitre IX, Hermann, Paris 1948
• Bourbaki, N.: Éléments de Mathématique, Livre II: Algèbre, Chapitre VIII, Hermann, Paris 1958
• Brauer, R.: Über Systeme hyperkomplexer Zahlen, Math. Z. 30\br(1929)\brr79–107
• Bremner, A.: Some cubic surfaces with no rational points, Math. Proc. Cambridge Philos. Soc. 84\br(1978)\brr219–223
• Bright, M. J.: Computations on diagonal quartic surfaces, Ph.D. thesis, Cambridge 2002
• Bright, M.: The Brauer-Manin obstruction on a general diagonal quartic surface, Acta Arith. 147\br(2011)\brr291–302
• Bright, M. J., Bruin, N., Flynn, E. V., and Logan, A.: The Brauer-Manin obstruction and \textcyr{Sh}$[2]$, LMS J. Comput. Math. 10\br(2007)\brr354–377
• Browning, T. D.: An overview of Manin’s conjecture for del Pezzo surfaces, in: Analytic number theory, Clay Math. Proc. 7, Amer. Math. Soc., Providence 2007, 39–55
• Browning, T. D. and Derenthal, U.: Manin’s conjecture for a quartic del Pezzo surface with $A_4$ singularity, Ann. Inst. Fourier 59\br(2009)\brr1231–1265
• Browning, T. D. and Derenthal, U.: Manin’s conjecture for a cubic surface with $D_5$ singularity, Int. Math. Res. Not. IMRN 2009\br(2009)\brr2620–2647
• Brüdern, J.: Einführung in die analytische Zahlentheorie, Springer, Berlin 1995
• Burgos Gil, J. I.: Arithmetic Chow rings, Ph.D. thesis, Barcelona 1994
• Burgos Gil, J. I., Kramer, J., and Kühn, U.: Cohomological arithmetic Chow rings, J. Inst. Math. Jussieu 6\br(2007)\brr1–172
• Cartan, E.: Œvres complètes, Partie II, Volume I: Nombres complexes, Gauthier-Villars, 107–246
• Cartan, H. and Eilenberg, S.: Homological Algebra, Princeton Univ. Press, Princeton 1956
• Cassels, J. W. S.: Bounds for the least solutions of homogeneous quadratic equations, Proc. Cambridge Philos. Soc. 51\br(1955)\brr262–264
• Cassels, J. W. S.: Global fields, in: Algebraic number theory, Edited by J. W. S. Cassels and A. Fröhlich, Academic Press and Thompson Book Co., London and Washington 1967
• Cassels, J. W. S. and Guy, M. J. T.: On the Hasse principle for cubic surfaces, Mathematika 13\br(1966)\brr111–120.
• Chambert-Loir, A.: Points de petite hauteur sur les variétés semi-abéliennes, Ann. Sci. École Norm. Sup. 33\br(2000)\brr789–821
• Chambert-Loir, A. and Tschinkel, Y.: On the distribution of points of bounded height on equivariant compactifications of vector groups, Invent. Math. 148\br(2002)\brr421–452
• Chase, S. U.: Two remarks on central simple algebras, Comm. in Algebra 12\br(1984)\brr2279–2289
• Châtelet, F.: Variations sur un thème de H. Poincaré, Annales E. N. S. 61\br(1944)\brr249–300
• Châtelet, F.: Géométrie diophantienne et théorie des algèbres, Séminaire Dubreil, 1954–55, exposé 17
• Clemens, C. H. and Griffiths, P. A.: The intermediate Jacobian of the cubic threefold, Annals of Math. 95\br(1972)\brr281–356
• Cohen, H.: A course in computational algebraic number theory, Graduate Texts in Mathematics 138, Springer, Berlin, Heidelberg 1993
• Cohen, H.: Advanced topics in computational number theory, Graduate Texts in Mathematics 193, Springer, New York 2000
• Colliot-Thélène, J.-L.: Hilbert’s theorem 90 for $K_{2}$, with application to the Chow group of rational surfaces, Invent. Math. 35\br(1983)\brr1–20
• Colliot-Thélène, J.-L.: Les grands thèmes de François Châtelet, L’Enseignement Mathématique 34\br(1988)\brr387–405
• Colliot-Thélène, J.-L.: Cycles algébriques de torsion et $K$-théorie algébrique, in: Arithmetic Algebraic Geometry (Trento 1991), Lecture Notes Math. 1553, Springer, Berlin, Heidelberg 1993, 1–49
• Colliot-Thélène, J.-L., Kanevsky, D., and Sansuc, J.-J.: Arithmétique des surfaces cubiques diagonales, in: Diophantine approximation and transcendence theory (Bonn 1985), Lecture Notes in Math. 1290, Springer, Berlin 1987, 1–108
• Colliot-Thélène, J.-L. and Sansuc, J.-J.: Torseurs sous des groupes de type multiplicatif, applications à l’étude des points rationnels de certaines variétés algébriques, C. R. Acad. Sci. Paris Sér I Math. 282\br(1976)\brr1113–1116
• Colliot-Thélène, J.-L. and Sansuc, J.-J.: On the Chow groups of certain rational surfaces: A sequel to a paper of S. Bloch, Duke Math. J. 48\br(1981)\brr421–447
• Colliot-Thélène, J.-L. and Sansuc, J.-J.: La descente sur les variétés rationnelles II, Duke Math. J. 54\br(1987)\brr375–492
• Colliot-Thélène, J.-L. and Skorobogatov, A. N.: Good reduction of the Brauer-Manin obstruction, Trans. Amer. Math. Soc. 365\br(2013)\brr579–590
• Colliot-Thélène, J.-L. and Swinnerton-Dyer, Sir Peter: Hasse principle and weak approximation for pencils of Severi-Brauer and similar varieties, J. für die Reine und Angew. Math. 453\br(1994)\brr49–112
• Cormen, T., Leiserson, C., and Rivest, R.: Introduction to algorithms, MIT Press and McGraw-Hill, Cambridge and New York 1990
• Corn, P. K.: Del Pezzo surfaces and the Brauer-Manin obstruction, Ph.D. thesis, Harvard 2005
• Cornell, G. and Silverman, J. H.: Arithmetic geometry, Papers from the conference held at the University of Connecticut, Springer, New York 1986
• Cox, D. A.: The homogeneous coordinate ring of a toric variety, J. Algebraic Geom. 4\br(1995)\brr17–50
• de la Bretèche, R.: Sur le nombre de points de hauteur bornée d’une certaine surface cubique singulière, Astérisque 251\br(1998)\brr51–77
• de la Bretèche, R.: Compter des points d’une variété torique, J. Number Theory 87\br(2001)\brr315–331
• de la Bretèche, R.: Nombre de points de hauteur bornée sur les surfaces de del Pezzo de degré 5, Duke Math. J. 113\br(2002)\brr421–464
• de la Bretèche, R.: Répartition de points rationnels sur la cubique de Segre, Proc. London Math. Soc. 95\br(2007)\brr69–155
• de la Bretèche, R. and Browning, T. D.: On Manin’s conjecture for singular del Pezzo surfaces of degree $4$ I, Michigan Math. J. 55\br(2007)\brr51–80
• de la Bretèche, R. and Browning, T. D.: On Manin’s conjecture for singular del Pezzo surfaces of degree four II, Math. Proc. Cambridge Philos. Soc. 143\br(2007)\brr579–605
• de la Bretèche, R. and Browning, T. D.: Manin’s conjecture for quartic del Pezzo surfaces with a conic fibration, Duke Math. J. 160\br(2011)\brr1–69
• de la Bretèche, R., Browning, T. D., and Derenthal, U.: On Manin’s conjecture for a certain singular cubic surface, Ann. Sci. École Norm. Sup. 40\br(2007)\brr1–50
• de la Bretèche, R., Browning, T. D., and Peyre, E.: On Manin’s conjecture for a family of Châtelet surfaces, Annals of Math. 175\br(2012)\brr297–343
• de la Bretèche, R. and Swinnerton-Dyer, Sir Peter: Fonction zêta des hauteurs associée à une certaine surface cubique, Bull. Soc. Math. France 135\br(2007)\brr65–92
• Deligne, P.: La conjecture de Weil I, Publ. Math. IHES 43\br(1974)\brr273–307
• Derenthal, U.: Geometry of universal torsors, Ph.D. thesis, Göttingen 2006
• Derenthal, U., Elsenhans, A.-S., and Jahnel, J.: On Peyre’s constant alpha for del Pezzo surfaces, Math. Comp. 83\br(2014)\brr965–977
• Derenthal, U. and Janda, F.: Gaussian rational points on a singular cubic surface, arXiv:1105.2807
• Derenthal, U. and Tschinkel, Y.: Universal torsors over del Pezzo surfaces and rational points, in: Equidistribution in number theory, an introduction, Springer, Dordrecht 2007, 169–196
• Deuring, M.: Algebren, Springer, Ergebnisse der Math. und ihrer Grenzgebiete, Berlin 1935
• Dickson, L. E.: Determination of all the subgroups of the known simple group of order $25\,920$, Trans. Amer. Math. Soc. 5\br(1904)\brr126–166
• Dickson, L. E.: On finite algebras, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Math.-Phys. Klasse, 1905, 358–393
• Dieudonné, J.: Foundations of modern analysis, Pure and Applied Mathematics, Volume 10-I, Academic Press, New York, London 1969
• Dieudonné, J.: Treatise on analysis, Volume II, Translated from the French by I. G. MacDonald, Enlarged and corrected printing, Pure and Applied Mathematics, Volume 10-II, Academic Press, New York, London 1976
• Dieudonné, J.: Treatise on analysis, Volume III, Translated from the French by I. G. MacDonald, Pure and Applied Mathematics, Volume 10-III, Academic Press, New York, London 1972
• Dokchitser, T.: Computing special values of motivic $L$-functions, Experiment. Math. 13\br(2004)\brr137–149
• Dolgachev, I. V.: Classical Algebraic Geometry: a modern view, Cambridge University Press, Cambridge 2012
• Draxl, P. K.: Skew fields, London Math. Soc. Lecture Notes Series 81, Cambridge University Press, Cambridge 1983
• Duke, W.: Extreme values of Artin $L$-functions and class numbers, Compositio Math. 136\br(2003)\brr103–115
• Edidin, D., Hassett, B., Kresch, A., and Vistoli, A.: Brauer groups and quotient stacks, Amer. J. Math. 123\br(2001)\brr761–777
• Ekedahl, T.: An effective version of Hilbert’s irreducibility theorem, in: Séminaire de Théorie des Nombres, Paris 1988–1989, Progr. Math. 91, Birkhäuser, Boston 1990, 241–249
• Grothendieck, A. et Dieudonné, J.: Éléments de Géométrie Algébrique, Publ. Math. IHES 4, 8, 11, 17, 20, 24, 28, 32\br(1960–68)
• Elkies, N. D.: Rational points near curves and small nonzero $|x^3 - y^2|$ via lattice reduction, in: Algorithmic number theory (Leiden 2000), Lecture Notes in Computer Science 1838, Springer, Berlin 2000, 33–63
• Elsenhans, A.-S. and Jahnel, J.: The Fibonacci sequence modulo $p^2$—An investigation by computer for $p < 10^{14}$, Preprint
• Elsenhans, A.-S. and Jahnel, J.: The Diophantine equation $x^ 4 + 2 y^ 4 = z^ 4 + 4 w^ 4$, Math. Comp. 75\br(2006)\brr935–940
• Elsenhans, A.-S. and Jahnel, J.: The Diophantine equation $x^ 4 + 2 y^ 4 = z^ 4 + 4 w^ 4$ — a number of improvements, Preprint
• Elsenhans, A.-S. and Jahnel, J.: The asymptotics of points of bounded height on diagonal cubic and quartic threefolds, in: Algorithmic number theory, Lecture Notes in Computer Science 4076, Springer, Berlin 2006, 317–332
• Elsenhans, A.-S. and Jahnel, J.: On the smallest point on a diagonal quartic threefold, J. Ramanujan Math. Soc. 22\br(2007)\brr189–204
• Elsenhans, A.-S. and Jahnel, J.: Experiments with general cubic surfaces, in: Tschinkel, Y. and Zarhin, Y. (Eds.): Algebra, Arithmetic, and Geometry, In Honor of Yu. I. Manin, Volume I, Progress in Mathematics 269, Birkhäuser, Boston 2007, 637–654
• Elsenhans, A.-S. and Jahnel, J.: On the smallest point on a diagonal cubic surface, Experimental Mathematics 19\br(2010)\brr181–193
• Elsenhans, A.-S. and Jahnel, J.: New sums of three cubes, Math. Comp. 78\br(2009)\brr1227–1230
• Elsenhans, A.-S. and Jahnel, J.: List of solutions of $x^3 + y^3 + z^3 = n$ for 𝑛<1 000 neither a cube nor twice a cube, Web page available at the URL: http://\discretionary{}www.uni-math.gwdg.de\discretionary{/}/jahnel\discretionary{/}/Arbeiten\discretionary{/}/Liste\discretionary{/}/threecubes_20070419.txt
• Elsenhans, A.-S. and Jahnel, J.: On the Brauer-Manin obstruction for cubic surfaces, Journal of Combinatorics and Number Theory 2\br(2010)\brr107–128
• Faltings, G.: Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73\br(1983)\brr349–366
• Faltings, G.: Calculus on arithmetic surfaces, Annals of Math. 119\br(1984)\brr387–424
• Faltings, G.: The general case of S. Lang’s conjecture, in: Barsotti Symposium in Algebraic Geometry (Abano Terme 1991), Perspect. Math. 15, Academic Press, San Diego 1994, 175–182
• Faltings, G.: Lectures on the arithmetic Riemann-Roch theorem, Annals of Mathematics Studies 127, Princeton University Press, Princeton 1992
• Fincke, U. and Pohst, M.: Improved methods for calculating vectors of short length in a lattice, including a complexity analysis, Math. Comp. 44\br(1985)\brr463–471
• Forster, O.: Algorithmische Zahlentheorie, Vieweg, Braunschweig 1996
• Fouvry, È.: Sur la hauteur des points d’une certaine surface cubique singulière, Astérisque 251\br(1998)\brr31–49
• Franke, J., Manin, Yu. I., and Tschinkel, Y.: Rational points of bounded height on Fano varieties, Invent. Math. 95\br(1989)\brr421–435
• Frei, C.: Counting rational points over number fields on a singular cubic surface, arXiv:1204.0383
• Fulton, W.: Intersection theory, Springer, Ergebnisse der Math. und ihrer Grenzgebiete, 3. Folge, Band 2, Berlin 1984
• Gabber, O.: Some theorems on Azumaya algebras, in: The Brauer group (Les Plans-sur-Bex 1980), Lecture Notes Math. 844, Springer, Berlin, Heidelberg, New York 1981, 129–209
• Gatsinzi, J.-B. and Tignol, J.-P.: Involutions and Brauer-Severi varieties, Indag. Math. 7\br(1996)\brr149–160
• Gelbart, S. S.: Automorphic forms on adéle groups, Annals of Mathematics Studies 83, Princeton University Press, Princeton 1975
• Gillet, H., Soulé, C.: Arithmetic intersection theory, Publ. Math. IHES 72\br(1990)\brr93-174
• Gillet, H., Soulé, C.: An arithmetic Riemann-Roch theorem, Invent. Math. 110\br(1992)\brr473–543
• Giraud, J.: Cohomologie non abélienne, Springer, Grundlehren der math. Wissenschaften 179, Berlin, Heidelberg, New York 1971
• Griffiths, P. and Harris, J.: Principles of algebraic geometry, John Wiley & Sons, New York 1978
• Grothendieck, A.: Le groupe de Brauer, I: Algèbres d’Azumaya et interprétations diverses, Séminaire Bourbaki, 17$^\textrm {e}$ année 1964/65, n$^\textrm {o}$ 290
• Grothendieck, A.: Le groupe de Brauer, II: Théorie cohomologique, Séminaire Bourbaki, 18$^\textrm {e}$ année 1965/66, n$^\textrm {o}$ 297
• Grothendieck, A.: Le groupe de Brauer, III: Exemples et compléments, in: Grothendieck, A.: Dix exposés sur la Cohomologie des schémas, North-Holland, Amsterdam and Masson, Paris 1968, 88–188
• Gruenberg, K.: Profinite groups, in: Algebraic number theory, Edited by J. W. S. Cassels and A. Fröhlich, Academic Press and Thompson Book Co., London and Washington 1967
• Haberland, K.: Galois cohomology of algebraic number fields, With two appendices by H. Koch and Th. Zink, VEB Deutscher Verlag der Wissenschaften, Berlin 1978
• Haile, D. E.: On central simple algebras of given exponent, J. of Algebra 57\br(1979)\brr449–465
• Handbook of numerical analysis, edited by P. G. Ciarlet and J. L. Lions, Vols. II–IV, North-Holland Publishing Co., Amsterdam 1991–1996
• Harari, D.: Méthode des fibrations et obstruction de Manin, Duke Math. J. 75\br(1994)\brr221–260
• Harari, D.: Obstructions de Manin transcendantes, in: Number theory (Paris 1993–1994), London Math. Soc. Lecture Note Ser. 235, Cambridge Univ. Press, Cambridge 1996, 75–87
• Hardy, G. H. and Wright, E. M.: An introduction to the theory of numbers, Fifth edition, Oxford University Press, New York 1979
• Hartshorne, R.: Ample subvarieties of algebraic varieties, Lecture Notes Math. 156, Springer, Berlin-New York 1970
• Hartshorne, R.: Algebraic Geometry, Graduate Texts in Mathematics 52, Springer, New York 1977
• Hassett, B. and Várilly-Alvarado, A.: Failure of the Hasse principle on general $K3$ surfaces, arXiv:1110.1738
• Hassett, B., Várilly-Alvarado, A., and Varilly, P.: Transcendental obstructions to weak approximation on general $K3$ surfaces, Adv. Math. 228\br(2011)\brr1377–1404
• Heath-Brown, D. R.: The density of zeros of forms for which weak approximation fails, Math. Comp. 59\br(1992)\brr613–623
• Heath-Brown, D. R.: Zero-free regions for Dirichlet $L$-functions, and the least prime in an arithmetic progression, Proc. London Math. Soc. 64\br(1992)\brr265–338
• Heath-Brown, D. R.: The density of rational points on Cayley’s cubic surface, Bonner Math. Schriften 360\br(2003)\brr1–33
• Heath-Brown, D. R., Lioen, W. M., and te Riele, H. J. J.: On solving the diophantine equation $x^3 + y^3 +z^3 = k$ on a vector computer, Math. Comp. 61\br(1993)\brr235–244
• Heath-Brown, D. R. and Moroz, B. Z.: The density of rational points on the cubic surface $X_0^3 = X_1X_2X_3$, Math. Proc. Cambridge Philos. Soc. 125\br(1999)\brr385–395
• Heilbronn, H.: Zeta-functions and $L$-functions, in: Algebraic number theory, Edited by J. W. S. Cassels and A. Fröhlich, Academic Press and Thompson Book Co., London and Washington 1967
• Hennessy, J. L. and Patterson, D. A.: Computer Architecture: A Quantitative Approach, 2$^\textrm {nd}$ ed., Morgan Kaufmann, San Mateo (CA) 1996
• Henningsen, F.: Brauer-Severi-Varietäten und Normrelationen von Symbolalgebren, Doktorarbeit (Ph. D. thesis), available in electronic form at http://www.\discretionary{}biblio.\discretionary{}tu-bs.de/ediss/ data/20000713a/20000713a.pdf
• Hermann, G.: Die Frage der endlich vielen Schritte in der Theorie der Polynomideale, Math. Ann. 95\br(1926)\brr736–788
• Herstein, I. N.: Noncommutative rings, The Math. Association of America (Inc.), distributed by John Wiley and Sons, Menasha, WI 1968
• Heuser, A.: Über den Funktionenkörper der Normfläche einer zentral einfachen Algebra, J. für die Reine und Angew. Math. 301\br(1978)\brr105–113
• Hirzebruch, F.: Der Satz von Riemann-Roch in Faisceau-theoretischer Formulierung: Einige Anwendungen und offene Fragen, Proc. Int. Cong. of Mathematicians, Amsterdam 1954, vol. III, 457–473, Erven P. Noordhoff N.V. and North-Holland Publishing Co., Groningen and Amsterdam 1956
• Hoffman, J. W. and Weintraub, S. H.: Four dimensional symplectic geometry over the field with three elements and a moduli space of abelian surfaces, Note Mat. 20\br(2000/01)\brr111–157
• Hoffmann, N., Jahnel, J., and Stuhler, U.: Generalized vector bundles on curves, J. für die Reine und Angew. Math. 495\br(1998)\brr35-60
• Hoobler, R. T.: A cohomological interpretation of Brauer groups of rings, Pacific J. Math. 86\br(1980)\brr89–92
• Ieronymou, E.: Diagonal quartic surfaces and transcendental elements of the Brauer groups, J. Inst. Math. Jussieu 9\br(2010)\brr769–798
• Ieronymou, E., Skorobogatov, A., and Zarhin, Yu.: On the Brauer group of diagonal quartic surfaces, With an appendix by Peter Swinnerton-Dyer, J. Lond. Math. Soc. 83\br(2011)\brr659–672
• Ireland, K. F. and Rosen, M. I.: A classical introduction to modern number theory, Graduate Texts in Mathematics 84, Springer, New York and Berlin 1982
• \textcyr{Iskovskih, V. A.: Kontrprimer k principu Khasse dlya sistemy dvukh kvadratichnykh form ot pyati peremennykh, Matematicheskie Zametki 10\br(1971)\brr253–257} English translation: Iskovskih, V. A.: A counterexample to the Hasse principle for systems of two quadratic forms in five variables, Mathematical Notes 10\br(1971)\brr575–577
• Jacobson, N.: Structure of rings, Revised edition, Amer. Math. Soc. Coll. Publ. 37, Amer. Math. Soc., Providence, R.I. 1964
• Jahnel, J.: Line bundles on arithmetic surfaces and intersection theory, Manuscripta Math. 91\br(1996)\brr103–119
• Jahnel, J.: Heights for line bundles on arithmetic varieties, Manuscripta Math. 96\br(1998)\brr421–442
• Jahnel, J.: A height function on the Picard group of singular Arakelov varieties, in: Algebraic K-Theory and Its Applications, Proceedings of the Workshop and Symposium held at ICTP Trieste, September 1997, edited by H. Bass, A. O. Kuku and C. Pedrini, World Scientific, Singapore 1999, 410–436
• Jahnel, J.: The Brauer-Severi variety associated with a central simple algebra, Linear Algebraic Groups and Related Structures 52\br(2000)\brr1–60
• Jahnel, J.: More cubic surfaces violating the Hasse principle, Journal de Théorie des Nombres de Bordeaux 23\br(2011)\brr471–477
• Jahnel, J.: On the distribution of small points on abelian and toric varieties, Preprint
• de Jong, A. J.: Smoothness, semi-stability and alterations, Publ. Math. IHES 83\br(1996)\brr51–93
• de Jong, A. J.: A result of Gabber, Preprint, available at the URL: http://www.math\discretionary{.}.columbia.edu\discretionary{/}/~dejong/papers/2-gabber.pdf
• Kempf, G., Knudsen, F. F., Mumford, D., and Saint-Donat, B.: Toroidal embeddings I, Lecture Notes in Mathematics 339, Springer, Berlin-New York 1973
• Kersten, I.: Brauergruppen von Körpern, Vieweg, Braunschweig 1990
• Kersten, I. and Rehmann, U.: Generic splitting of reductive groups, Tôhoku Math. J. 46\br(1994)\brr35–70
• Knus, M. A. and Ojanguren, M.: Théorie de la descente et algèbres d’Azumaya, Springer, Lecture Notes Math. 389, Berlin, Heidelberg, New York 1974
• Knus, M. A. and Ojanguren, M.: Cohomologie étale et groupe de Brauer, in: The Brauer group (Les Plans-sur-Bex 1980), Lecture Notes Math. 844, Springer, Berlin, Heidelberg, New York 1981, 210–228
• Kresch, A. and Tschinkel, Y.: Effectivity of Brauer-Manin obstructions, Preprint
• Kress, R.: Numerical analysis, Graduate Texts in Mathematics 181, Springer, New York 1998
• Laface, A. and Velasco, M.: A survey on Cox rings, Geom. Dedicata 139\br(2009)\brr269–287
• Lang, S.: Hyperbolic and Diophantine analysis, Bull. Amer. Math. Soc. 14\br(1986)\brr159–205
• Lang, S.: Algebra, Third Edition, Addison-Wesley, Reading, MA 1993
• \textcyr{Lavrik, A. F.: O funkcionalp1nykh uravneniyakh funkciĭ Dirikhle, Izv. Akad. Nauk SSSR, Ser. Mat. 31\br(1967)\brr431–442} English translation: Lavrik, A. F.: On functional equations of Dirichlet functions, Math. USSR-Izv. 31\br(1967)\brr421–432
• Lazarsfeld, R.: Positivity in algebraic geometry I, Ergebnisse der Mathematik und ihrer Grenzgebiete (3. Folge) 48, Springer, Berlin 2004
• Le Boudec, P.: Manin’s conjecture for a cubic surface with $2A_2+A_1$ singularity type, Math. Proc. Cambridge Philos. Soc. 153\br(2012)\brr419–455
• Le Boudec, P.: Manin’s conjecture for a quartic del Pezzo surface with $A_3$ singularity and four lines, Monatsh. Math. 167\br(2012)\brr481–502
• Le Boudec, P.: Manin’s conjecture for two quartic del Pezzo surfaces with $3A_1$ and $A_1+A_2$ singularity types, Acta Arith. 151\br(2012)\brr109–163
• Lelong, P.: Fonctions plurisousharmoniques et formes différentielles positives, Gordon & Breach, Paris 1968
• Lichtenbaum, S.: Duality theorems for curves over $p$-adic fields, Invent. Math. 7\br(1969)\brr120–136
• Lind, C.-E.: Untersuchungen über die rationalen Punkte der ebenen kubischen Kurven vom Geschlecht Eins, Doktorarbeit (Ph.D. thesis), Uppsala 1940
• Lorenz, F. and Opolka, H.: Einfache Algebren und projektive Darstellungen über Zahlkörpern, Math. Z. 162\br(1978)\brr175–182
• Loughran, D.: Manin’s conjecture for a singular sextic del Pezzo surface, Journal de Théorie des Nombres de Bordeaux 22\br(2010)\brr675–701
• Loughran, D.: Manin’s conjecture for a singular quartic del Pezzo surface, J. London Math. Soc. 86\br(2012)\brr558–584
• Lovász, L.: How to compute the volume?, Jahresbericht der DMV, Jubiläumstagung 100 Jahre DMV (Bremen 1990), 138–151
• Maclagan-Wedderburn, J. H.: A theorem on finite algebras, Trans. Amer. Math. Soc. 6\br(1905)\brr349–352
• Maclagan-Wedderburn, J. H.: On hypercomplex numbers, Proc. London Math. Soc., 2nd Series, 6\br(1908)\brr77–118
• \textcyr{Manin, Yu. I.: Kubicheskie formy: algebra, geometriya, arifmetika, Nauka, Moskva 1972} English translation: Manin, Yu. I.: Cubic forms, algebra, geometry, arithmetic, North-Holland Publishing Co. and American Elsevier Publishing Co., Amsterdam-London and New York 1974
• Marcus, D. A.: Number fields, Springer, New York - Heidelberg 1977
• Matsumura, H.: Commutative ring theory, Cambridge Studies in Advanced Mathematics 8, Cambridge University Press, Cambridge 1986
• McKinnon, D.: Counting rational points on $K3$ surfaces, J. Number Theory 84\br(2000)\brr49–62
• McKinnon, D.: Vojta’s conjecture implies the Batyrev-Manin conjecture for $K3$ surfaces, Bull. Lond. Math. Soc. 43\br(2011)\brr1111–1118
• O’Meara, O. T.: Introduction to quadratic forms, Springer, Berlin, New York 1963
• Merkurjev, A. S.: Brauer groups of fields, Comm. in Algebra 11\br(1983)\brr2611–2624
• \textcyr{Merkurp1ev, A. S.: O stroenii gruppy Braue1ra poleĭ, Izv. Akad. Nauk SSSR Ser. Mat. 49\br(1985)\brr828–846,} English translation: Merkurjev, A. S.: Structure of the Brauer group of fields, Math. USSR-Izv. 27\br(1986)\brr141–157
• \textcyr{Merkurp1ev, A. S.: Zamknutye tochki mnogoobraziĭ Severi-Braue1ra, Vestnik S.-Peterburg. Univ. Mat. Mekh. Astronom. 1993-2\br(1993)\brr51–53} English translation: Merkurjev, A. S.: Closed points of Brauer-Severi varieties, Vestnik St. Petersburg Univ. Math. 26-2\br(1993)\brr44–46
• \textcyr{Merkurp1ev, A. S. i Suslin, A. A.: $K$-kogomologii mnogoobraziĭ Severi-Braue1ra i gomomorfizm normennogo vycheta, Izv. Akad. Nauk SSSR Ser. Mat. 46\br(1982)\brr1011–1046,} English translation: Merkurjev, A. S. and Suslin, A. A.: $K$-cohomology of Severi-Brauer varieties and the norm residue homomorphism, Math. USSR-Izv. 21\br(1983)\brr307–340
• de Meyer, F. and Ford, T. J.: On the Brauer group of surfaces and subrings of $k[x,y]$, in: van Oystaeyen, F. and Verschoren, A. (Eds.): Brauer groups in ring theory and algebraic geometry, Proceedings of a conference held at Antwerp 1981, Lecture Notes Math. 917, Springer, Berlin, Heidelberg, New York 1982, 211–221
• de Meyer, F. and Ingraham, E.: Separable algebras over commutative rings, Lecture Notes Math. 181, Springer, Berlin, Heidelberg, New York 1971
• Milne, J. S.: Étale Cohomology, Princeton University Press, Princeton 1980
• Molien, T.: Über Systeme höherer complexer Zahlen, Math. Ann. 41\br(1893)\brr83–156
• Mordell, L. J.: On the conjecture for the rational points on a cubic surface, J. London Math. Soc. 40\br(1965)\brr149–158
• Morita, Y.: Remarks on a conjecture of Batyrev and Manin, Tohoku Math. J. 49\br(1997)\brr437–448
• Moriwaki, A.: Intersection pairing for arithmetic cycles with degenerate Green currents, E-print AG/9803054
• Murre, J. P.: Algebraic equivalence modulo rational equivalence on a cubic threefold, Compositio Math. 25\br(1972)\brr161–206
• Murty, M. R.: Applications of symmetric power $L$-functions, in: Lectures on automorphic $L$-functions, Fields Inst. Monogr. 20, Amer. Math. Soc., Providence 2004, 203–283
• Nakayama, T.: Divisionsalgebren über diskret bewerteten perfekten Körpern, J. für die Reine und Angew. Math. 178\br(1937)\brr11–13
• Nathanson, M. B.: Elementary methods in number theory, Graduate Texts in Mathematics 195, Springer, New York 2000
• Neukirch, J.: Algebraic number theory, Grundlehren der Mathematischen Wissenschaften 322, Springer, Berlin 1999
• Noether, M.: Rationale Ausführung der Operationen in der Theorie der algebraischen Funktionen, Math. Ann. 23\br(1884)\brr311–358
• Orzech, M.: Brauer Groups and Class Groups for a Krull Domain, in: van Oystaeyen, F. and Verschoren, A. (Eds.): Brauer groups in ring theory and algebraic geometry, Proceedings of a conference held at Antwerp 1981, Lecture Notes Math. 917, Springer, Berlin, Heidelberg, New York 1982, 66–90
• Orzech, M. and Small, C.: The Brauer group of commutative rings: Brauer-Manin obstruction, Lecture Notes in Pure and Applied Mathematics 11, Marcel Dekker, New York 1975
• Orzech, M. and Verschoren, A.: Some remarks on Brauer groups of Krull domains, in: van Oystaeyen, F. and Verschoren, A. (Eds.): Brauer groups in ring theory and algebraic geometry, Proceedings of a conference held at Antwerp 1981, Lecture Notes Math. 917, Springer, Berlin, Heidelberg, New York 1982, 91–95
• Peyre, E.: Hauteurs et mesures de Tamagawa sur les variétés de Fano, Duke Math. J. 79\br(1995)\brr101–218
• Peyre, E.: Products of Severi-Brauer varieties and Galois cohomology, in: Proc. Symp. Pure Math. 58, Part 2: $K$-theory and algebraic geometry: connections with quadratic forms and division algebras (Santa Barbara, CA 1992), Amer. Math. Soc., Providence, R.I. 1995, 369–401
• Peyre, E.: Points de hauteur bornée et géométrie des variétés (d’après Y. Manin et al.), Séminaire Bourbaki 2000/2001, Astérisque 282\br(2002)\brr323–344
• Peyre, E.: Points de hauteur bornée, topologie adélique et mesures de Tamagawa, Journal de Théorie des Nombres de Bordeaux 15\br(2003)\brr319–349
• Peyre, E. and Tschinkel, Y.: Tamagawa numbers of diagonal cubic surfaces, numerical evidence, Math. Comp. 70\br(2001)\brr367–387
• Pierce, R. S.: Associative Algebras, Graduate Texts in Mathematics 88, Springer, New York 1982
• Pohst, M. and Zassenhaus, H.: Algorithmic algebraic number theory, Encyclopedia of Mathematics and its Applications 30, Cambridge University Press, Cambridge 1989
• Poincaré, H.: Sur les propriétés arithmétiques des courbes algébriques, J. Math. Pures et Appl. 5$^{e}$ série, 7\br(1901)\brr161–234
• Poonen, B.: Insufficiency of the Brauer-Manin obstruction applied to éétale covers, Annals of Math. 171\br(2010)\brr2157–2169
• Poonen, B. and Tschinkel, Y. (eds.): Arithmetic of higher-dimensional algebraic varieties, Proceedings of the Workshop on Rational and Integral Points of Higher-Dimensional Varieties held in Palo Alto, CA, December 11–20, 2002, Birkhäuser, Progress in Mathematics 226, Boston 2004
• Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T.: Numerical recipes, The art of scientific computing, Cambridge University Press, Cambridge 1986
• Preu, T.: Transcendental Brauer-Manin Obstruction for a Diagonal Quartic Surface, Ph.D. thesis, Zürich 2010
• Quillen, D.: Higher algebraic $K$-theory I, in: Algebraic $K$-theory I, Higher $K$-theories, Lecture Notes Math. 341, Springer, Berlin, Heidelberg, New York 1973, 85–147
• Reiner, I.: Maximal orders, Academic Press, London-New York 1975
• Robbiani, M.: On the number of rational points of bounded height on smooth bilinear hypersurfaces in biprojective space, J. London Math. Soc. 63\br(2001)\brr33–51
• Roquette, P.: On the Galois cohomology of the projective linear group and its applications to the construction of generic splitting fields of algebras, Math. Ann. 150\br(1963)\brr411–439
• Roquette, P.: Isomorphisms of generic splitting fields of simple algebras, J. für die Reine und Angew. Math. 214/215\br(1964)\brr207–226
• Roux, B.: Sur le groupe de Brauer d’un corps local à corps résiduel imparfait, in: Groupe d’Etude d’Analyse Ultramétriuqe, Publ. Math. de l’Univ. de Paris VII 29\br(1985/86)\brr85–97
• Salberger, P.: Tamagawa measures on universal torsors and points of bounded height on Fano varieties, Astérisque 251\br(1998)\brr91–258
• Saltman, P. J.: Division algebras over discrete valued fields, Comm. in Algebra 8\br(1980)\brr1749–1774
• Saltman, P. J.: The Brauer group is torsion, Proc. Amer. Math. Soc. 81\br(1981)\brr385–387
• Satake, I.: On the structure of Brauer group of a discretely valued complete field, Sci. Papers Coll. Gen. Ed. Univ. Tokyo 1\br(1951)\brr1–10
• Schanuel, S.: On heights in number fields, Bull. Amer. Math. Soc. 70\br(1964)\brr262–263
• Scharlau, W.: Quadratic and Hermitian forms, Springer, Grundlehren der Math. Wissenschaften 270, Berlin, Heidelberg, New York 1985
• Schindler, D.: On Diophantine equations involving norm forms and bihomogenous forms, Ph.D. thesis, Bristol 2013
• Schindler, D.: Manin’s conjecture for certain biprojective hypersurfaces, arXiv:\discretionary{}1307.\discretionary{}7069
• Schmidt, W. M.: The density of integer points on homogeneous varieties, Acta Math. 154\br(1985)\brr243–296
• Schönhage, A. and Strassen, V.: Schnelle Multiplikation großer Zahlen, Computing 7\br(1971)\brr281–292
• Schröer, S.: There are enough Azumaya algebras on surfaces, Math. Ann. 321\br(2001)\brr439–454
• Schwarz, H. A.: Sur une définition erronée de l’aire d’une surface courbe, Communication faite à M. Charles Hermite, 1881–82, in: Gesammelte Mathematische Abhandlungen, Zweiter Band, Springer, Berlin 1890, 309–311
• Sedgewick, R.: Algorithms, Addison-Wesley, Reading 1983
• Seelinger, G.: A description of the Brauer-Severi scheme of trace rings of generic matrices, J. of Algebra 184\br(1996)\brr852–880
• Seelinger, G.: Brauer-Severi schemes of finitely generated algebras, Israel J. Math. 111\br(1999)\brr321–337
• Selmer, E. S.: The Diophantine equation $ax^ 3+by^ 3+cz^ 3=0$, Acta Math. 85\br(1951)\brr203–362
• Serre, J.-P.: Corps locaux, Hermann, Paris 1962
• Serre, J.-P.: Local class field theory, in: Algebraic number theory, Edited by J. W. S. Cassels and A. Fröhlich, Academic Press and Thompson Book Co., London and Washington 1967
• Serre, J.-P.: Propriétés galoisiennes des points d’ordre fini des courbes elliptiques, Invent. Math. 15\br(1972)\brr259–331
• Serre, J.-P.: Cohomologie Galoisienne, Lecture Notes in Mathematics 5, Quatrième Edition, Springer, Berlin 1973
• Severi, F.: Un nuovo campo di richerche nella geometria sopra una superficie e sopra una varietà algebrica, Mem. della Acc. R. d’Italia 3\br(1932)\brr1–52 = Opere matematiche, vol. terzo, Acc. Naz. Lincei, Roma, 541–586
• Demazure, A. et Grothendieck, A.: Schemas en groupes, Séminaire de Géométrie Algébrique du Bois Marie 1962–64 (SGA 3), Lecture Notes Math. 151, 152, 153, Springer, Berlin, Heidelberg, New York 1970
• Artin, M., Grothendieck, A. et Verdier, J.-L. (avec la collaboration de Deligne, P. et Saint-Donat, B.): Théorie des topos et cohomologie étale des schémas, Séminaire de Géométrie Algébrique du Bois Marie 1963–1964 (SGA 4), Lecture Notes in Math. 269, 270, 305, Springer, Berlin, Heidelberg, New York 1973
• Deligne, P. (avec la collaboration de Boutot, J. F., Grothendieck, A., Illusie, L. et Verdier, J. L.): Cohomologie Étale, Séminaire de Géométrie Algébrique du Bois Marie (SGA 4$\frac {1}{2}$), Lecture Notes Math. 569, Springer, Berlin, Heidelberg, New York 1977
• Berthelot, P., Grothendieck, A. et Illusie, L. (Avec la collaboration de Ferrand, D., Jouanolou, J. P., Jussila, O., Kleiman, S., Raynaud, M. et Serre, J. P.): Théorie des intersections et théorème de Riemann-Roch, Séminaire de Géométrie Algébrique du Bois Marie 1966-67 (SGA 6), Lecture Notes in Math. 225, Springer, Berlin-New York 1971
• Siegel, C. L.: Analytische Zahlentheorie, Teil II, Vorlesung, ausgearbeitet von K. F. Kürten und G. Köhler, Universität Göttingen 1963/64
• Siegel, C. L.: Abschätzung von Einheiten, Nachr. Akad. Wiss. Göttingen, Math.-Phys. Kl. II 1969\br(1969)\brr71–86
• Siegel, C. L.: Normen algebraischer Zahlen, Nachr. Akad. Wiss. Göttingen, Math.-Phys. Kl. II 1973\br(1973)\brr197–215
• Sims, C. C.: Computational methods in the study of permutation groups, in: Computational Problems in Abstract Algebra (Proc. Conf., Oxford 1967), Pergamon, Oxford 1970, 169–183
• Skorobogatov, A.: Torsors and rational points, Cambridge Tracts in Mathematics 144, Cambridge University Press, Cambridge 2001
• Skorobogatov, A. N. and Zarhin, Yu. G.: The Brauer group of Kummer surfaces and torsion of elliptic curves, J. Reine Angew. Math. 666\br(2012)\brr115–140
• Skorobogatov, A. and Swinnerton-Dyer, Sir Peter: $2$-descent on elliptic curves and rational points on certain Kummer surfaces, Adv. Math. 198\br(2005)\brr448–483
• Slater, J. B. and Swinnerton-Dyer, Sir Peter: Counting points on cubic surfaces I, in: Nombre et répartition de points de hauteur bornée (Paris 1996), Astérisque 251\br(1998)\brr1–12
• Smart, N. P.: The algorithmic resolution of Diophantine equations, London Mathematical Society Student Texts 41, Cambridge University Press, Cambridge 1998
• Soulé, C., Abramovich, D., Burnol, J.-F., and Kramer, J.: Lectures on Arakelov geometry, Cambridge Studies in Advanced Mathematics 8, Cambridge University Press, Cambridge 1992
• Spanier, E. H.: Algebraic topology, McGraw-Hill, New York-Toronto-London 1966
• Stark, H. M.: Some effective cases of the Brauer-Siegel theorem, Invent. Math. 23\br(1974)\brr135–152
• Stark, H. M.: Class fields for real quadratic fields and $L$-series at $1$, in: Algebraic number fields: $L$-functions and Galois properties (Proc. Sympos., Durham, 1975), Academic Press, London 1977, 355–375
• Strauch, M. and Tschinkel, Y.: Height zeta functions of twisted products, Math. Res. Lett. 4\br(1997)\brr273–282
• \textcyr{Suslin, A. A.: Kvaternionnyĭ gomomorfizm dlya polya funktsiĭ na konike, Dokl. Akad. Nauk SSSR 265\br(1982)\brr292–296,} English translation: Suslin, A. A.: The quaternion homomorphism for the function field on a conic, Soviet Math. Dokl. 26\br(1982)\brr72–77
• Swiȩcicka, J.: Small deformations of Brauer-Severi schemes, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26\br(1978)\brr591–593
• Swinnerton-Dyer, Sir Peter: Two special cubic surfaces, Mathematika 9\br(1962)\brr54–56
• Swinnerton-Dyer, Sir Peter: The Brauer group of cubic surfaces, Math. Proc. Cambridge Philos. Soc. 113\br(1993)\brr449–460
• Swinnerton-Dyer, Sir Peter: Rational points on fibered surfaces, in: Tschinkel, Y. (ed.): Mathematisches Institut, Seminars 2004, Universitätsverlag, Göttingen 2004, 103–109
• Swinnerton-Dyer, Sir Peter: Counting points on cubic surfaces II, in: Geometric methods in algebra and number theory, Progr. Math. 235, Birkhäuser, Boston 2005, 303–309
• Szeto, G.: Splitting Rings for Azumaya Quaternion Algebras, in: van Oystaeyen, F. and Verschoren, A. (Eds.): Brauer groups in ring theory and algebraic geometry, Proceedings of a conference held at Antwerp 1981, Lecture Notes Math. 917, Springer, Berlin, Heidelberg, New York 1982, 118–125
• Szpiro, L.: Sur les propriétés numériques du dualisant relatif d’une surface arithmétique, The Grothendieck Festschrift, vol. III, Birkhäuser, Boston 1990
• Szpiro, L., Ullmo, E., Zhang, S.: Equirépartition des petits points, Invent. Math. 127\br(1997)\brr337-347
• Tate, J.: Global class field theory, in: Algebraic number theory, Edited by J. W. S. Cassels and A. Fröhlich, Academic Press and Thompson Book Co., London and Washington 1967
• Tate, J.: Algorithm for determining the type of a singular fiber in an elliptic pencil, Modular functions of one variable IV (Proc. Internat. Summer School, Antwerp 1972), Lecture Notes in Math. 476, Springer, Berlin 1975, 33–52
• Tignol, J.-P.: Sur les decompositions des algèbres à divisions en produit tensoriel d’algèbres cycliques, in: van Oystaeyen, F. and Verschoren, A. (Eds.): Brauer groups in ring theory and algebraic geometry, Proceedings of a conference held at Antwerp 1981, Lecture Notes Math. 917, Springer, Berlin, Heidelberg, New York 1982, 126–145
• Tignol, J.-P.: On the corestriction of central simple algebras, Math. Z. 194\br(1987)\brr267–274
• \textcyr{Tregub, S. L.: O biratsionalp1noĭ e1kvivalentnosti mnogoobraziĭ Braue1ra-Severi, Uspekhi Mat. Nauk 46-6\br(282)\br(1991)\brr217–218} English translation: Tregub, S. L.: On the birational equivalence of Brauer-Severi varieties, Russian Math. Surveys 46-6\br(1991)\brr229
• Turner, S.: The zeta function of a birational Severi-Brauer scheme, Bol. Soc. Brasil. Mat. 10\br(1979)\brr25–50
• Ullmo, E.: Positivité et discrétion des points algébriques des courbes, Annals of Math. 147\br(1998)\brr167-179
• Vaughan, R. C.: The Hardy-Littlewood method, Cambridge Tracts in Mathematics 80, Cambridge University Press, Cambridge 1981
• Verschoren, A.: A check list on Brauer groups, in: van Oystaeyen, F. and Verschoren, A. (Eds.): Brauer groups in ring theory and algebraic geometry, Proceedings of a conference held at Antwerp 1981, Lecture Notes Math. 917, Springer, Berlin, Heidelberg, New York 1982, 279–300
• Wang, S.: On the commutator group of a simple algebra, Amer. J. Math. 72\br(1950)\brr323–334
• Warner, F. W.: Foundations of differentiable manifolds and Lie groups, Scott, Foresman and Co., Glenview-London 1971
• Weil, A.: Sur les courbes algébriques et les variétés qui s’en déduisent, Actualités Sci. Ind. 1041, Hermann et Cie., Paris 1948
• Weil, A.: The field of definition of a variety, Amer. J. of Math. 78\br(1956)\brr509–524
• Weyl, H.: Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77\br(1916)\brr313–352
• Witt, E.: Über ein Gegenbeispiel zum Normensatz, Math. Z. 39\br(1935)\brr462–467
• Witt, E.: Schiefkörper über diskret bewerteten Körpern, J. für die Reine und Angew. Math. 176\br(1937)\brr153–156
• Wittenberg, O.: Transcendental Brauer-Manin obstruction on a pencil of elliptic curves, in: Arithmetic of higher-dimensional algebraic varieties (Palo Alto 2002), Progr. Math. 226, Birkhäuser, Boston 2004, 259–267
• \textcyr{Yanchevskiĭ, V. I.: Printsip Khasse dlya grupp Braue1ra poleĭ funktsiĭ na proizveeniyakh mnogoobraziĭ Severi-Braue1ra i proektivnykh kvadrik, Trudy Mat. Inst. imeni Steklova 208\br(1995)\brr350–365}
• Yuan, S.: On the Brauer groups of local fields, Annals of Math. 82\br(1965)\brr434–444
• Zak, F. L.: Tangents and secants of algebraic varieties, AMS Translations of Mathematical Monographs 127, Amer. Math. Soc., Providence 1993
• Zhang, S.: Small points and adelic metrics, J. Alg. Geom. 4\br(1995)\brr281-300
• Zhang, S.: Positive line bundles on arithmetic varieties, J. Amer. Math. Soc. 8\br(1995)\brr187-221
• Zhang, S.: Equidistribution of small points on abelian varieties, Annals of Math. 147\br(1998)\brr159-165

\frenchspacing

• Abbes, A. and Bouche, T.: Théorème de Hilbert-Samuel “arithmétique”, Ann. Inst. Fourier 45\br(1995)\brr375–401
• Abramovich, D. and Voloch, J. F.: Lang’s conjectures, fibered powers, and uniformity, New York J. Math. 2\br(1996)\brr20–34
• Albert, A.: Structure of Algebras, Revised Printing, Amer. Math. Soc. Coll. Pub., Vol. XXIV, Amer. Math. Soc., Providence, R.I. 1961
• Software Optimization Guide for AMD Athlon$^\textrm {TM}$ 64 and AMD Opteron$^\textrm {TM}$ Processors, Rev. 3.04, AMD, Sunnyvale (CA) 2004
• Amitsur, S. A.: Generic splitting fields of central simple algebras, Annals of Math. 62\br(1955)\brr8–43
• Amitsur, S. A.: On central division algebras, Israel J. Math. 12\br(1972)\brr408–420
• Amitsur, S. A.: Generic splitting fields, in: van Oystaeyen, F. and Verschoren, A. (Eds.): Brauer groups in ring theory and algebraic geometry, Proceedings of a conference held at Antwerp 1981, Lecture Notes Math. 917, Springer, Berlin, Heidelberg, New York 1982, 1–24
• Apéry, F.: Models of the real projective plane, Vieweg, Braunschweig 1987
• Apostol, T. M.: Introduction to analytic number theory, Springer, New York-Heidelberg 1976
• \textcyr{Arakelov, S. Yu.: Teoriya peresecheniĭ divizorov na arifmeticheskoĭ poverkhnosti, Izv. Akad. Nauk SSSR, Ser. Mat. 38\br(1974)\brr1179–1192,} English translation: Arakelov, S. Yu.: Intersection theory of divisors on an arithmetic surface, Math. USSR Izv. 8\br(1974)\brr1167–1180
• Artin, E.: Über einen Satz von J. H. Maclagan-Wedderburn, Abh. Math. Sem. Univ. Hamburg 5\br(1927)\brr245–250
• Artin, E.: Zur Theorie der hyperkomplexen Zahlen, Abh. Math. Sem. Univ. Hamburg 5\br(1927)\brr251–260
• Artin, E., Nesbitt, C. J., and Thrall, R.: Rings with minimum condition, Univ. of Michigan Press, Ann Arbor 1948
• Artin, M.: Left Ideals in Maximal Orders, in: van Oystaeyen, F. and Verschoren, A. (Eds.): Brauer groups in ring theory and algebraic geometry, Proceedings of a conference held at Antwerp 1981, Lecture Notes Math. 917, Springer, Berlin, Heidelberg, New York 1982, 182–193
• Artin, M. (Notes by Verschoren, A.): Brauer-Severi varieties, in: van Oystaeyen, F. and Verschoren, A. (Eds.): Brauer groups in ring theory and algebraic geometry, Proceedings of a conference held at Antwerp 1981, Lecture Notes Math. 917, Springer, Berlin, Heidelberg, New York 1982, 194–210
• Artin, M. and Mumford, D.: Some elementary examples of unirational varieties which are not rational, Proc. London Math. Soc. 25\br(1972)\brr75–95
• Atiyah, M. F. and Wall, C. T. C.: Cohomomology of groups, in: Algebraic number theory, Edited by J. W. S. Cassels and A. Fröhlich, Academic Press and Thompson Book Co., London and Washington 1967
• Auslander, M. and Goldman, O.: The Brauer group of a commutative ring, Trans. Amer. Math. Soc. 97\br(1960)\brr367–409
• Azumaya, G.: On maximally central algebras, Nagoya Math. J. 2\br(1951)\brr119–150
• Barth, W., Hulek, K., Peters, C., and Van de Ven, A.: Compact complex surfaces, Second edition, Springer, Berlin 2004
• Batyrev, V. V. and Manin, Yu. I.: Sur le nombre des points rationnels de hauteur borné des variétés algébriques, Math. Ann. 286\br(1990)\brr27–43
• Batyrev, V. V. and Tschinkel, Y.: Rational points on some Fano cubic bundles, C. R. Acad. Sci. Paris 323\br(1996)\brr41–46
• Batyrev, V. V. and Tschinkel, Y.: Manin’s conjecture for toric varieties, J. Algebraic Geom. 7\br(1998)\brr15–53
• Beauville, A.: Complex algebraic surfaces, LMS Lecture Note Series 68, Cambridge University Press, Cambridge 1983
• Beck, M., Pine, E., Tarrant, W., and Yarbrough Jensen, K.: New integer representations as the sum of three cubes, Math. Comp. 76\br(2007)\brr1683–1690
• van den Bergh, M.: The Brauer-Severi scheme of the trace ring of generic matrices, in: Perspectives in ring theory (Antwerp 1987), NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 233, Kluwer Acad. Publ., Dordrecht 1988, 333–338
• Bernstein, D. J.: Enumerating solutions to $p(a)+q(b)=r(c)+s(d)$, Math. Comp. 70\br(2001)\brr389–394
• Bernstein, D. J.: threecubes, Web page available at the URL: http://\discretionary{}cr.yp.to/\discretionary{}threecubes.html
• Bertuccioni, I.: Brauer groups and cohomology, Arch. Math. 84\br(2005)\brr406–411
• Białynicki-Birula, A.: A note on deformations of Severi-Brauer varieties and relatively minimal models of fields of genus $0$, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 18\br(1970)\brr175–176
• \textcyr{Belotserkovski, Yu. F. [Bilu, Yu.]: Ravnomernoe raspredelenie algebraicheskikh chisel blizkikh k edinichnomu krugu, Vestsi1 Akad. Navuk BSSR, Ser. Fi1z.-Mat. Navuk 1988\br(1988)\brr49-52, 124}
• Bhowmik, G., Essouabri, D. and Lichtin, B.: Meromorphic continuation of multivariable Euler products, Forum Math. 19\br(2007)\brr1111–1139
• Bilu, Yu.: Limit distribution of small points on algebraic tori, Duke Math. J. 89\br(1997)\brr465-476
• Billard, H.: Propriétés arithmétiques d’une famille de surfaces $K3$, Compositio Math. 108\br(1997)\brr247–275
• Birch, B. J.: Forms in many variables, Proc. Roy. Soc. Ser. A 265\br(1961/1962)\brr245–263
• Blanchard, A.: Les corps non commutatifs, Presses Univ. de France, Vendôme 1972
• Blanchet, A.: Function fields of generalized Brauer-Severi varieties, Comm. in Algebra 19\br(1991)\brr97–118
• Blomer, V., Brüdern, J., and Salberger, P.: On a senary cubic form, arXiv:1205.0190
• Bogomolov, F. and Tschinkel, Y.: Rational curves and points on $K3$ surfaces, Amer. J. Math. 127\br(2005)\brr825–835
• Bombieri, E.: Problems and results on the distribution of algebraic points on algebraic varieites, Journal de Théorie des Nombres de Bordeaux 21\br(2009)\brr41–57
• \textcyr{Borevich, Z. I. i Shafarevich, I. R.: Teoriya chisel, Tretp1e izdanie, Nauka, Moskva 1985} English translation: Borevich, Z. I. and Shafarevich, I. R.: Number theory, Academic Press, New York-London 1966
• Bost, J.-B., Gillet, H., Soulé, C.: Heights of projective varieties and positive Green forms, J. Amer. Math. Soc. 7\br(1994)\brr903-1027
• Bott, R.: On a theorem of Lefschetz, Michigan Math. J. 6\br(1959)\brr211–216
• Bourbaki, N.: Éléments de Mathématique, Livre III: Topologie générale, Chapitre IX, Hermann, Paris 1948
• Bourbaki, N.: Éléments de Mathématique, Livre II: Algèbre, Chapitre VIII, Hermann, Paris 1958
• Brauer, R.: Über Systeme hyperkomplexer Zahlen, Math. Z. 30\br(1929)\brr79–107
• Bremner, A.: Some cubic surfaces with no rational points, Math. Proc. Cambridge Philos. Soc. 84\br(1978)\brr219–223
• Bright, M. J.: Computations on diagonal quartic surfaces, Ph.D. thesis, Cambridge 2002
• Bright, M.: The Brauer-Manin obstruction on a general diagonal quartic surface, Acta Arith. 147\br(2011)\brr291–302
• Bright, M. J., Bruin, N., Flynn, E. V., and Logan, A.: The Brauer-Manin obstruction and \textcyr{Sh}$[2]$, LMS J. Comput. Math. 10\br(2007)\brr354–377
• Browning, T. D.: An overview of Manin’s conjecture for del Pezzo surfaces, in: Analytic number theory, Clay Math. Proc. 7, Amer. Math. Soc., Providence 2007, 39–55
• Browning, T. D. and Derenthal, U.: Manin’s conjecture for a quartic del Pezzo surface with $A_4$ singularity, Ann. Inst. Fourier 59\br(2009)\brr1231–1265
• Browning, T. D. and Derenthal, U.: Manin’s conjecture for a cubic surface with $D_5$ singularity, Int. Math. Res. Not. IMRN 2009\br(2009)\brr2620–2647
• Brüdern, J.: Einführung in die analytische Zahlentheorie, Springer, Berlin 1995
• Burgos Gil, J. I.: Arithmetic Chow rings, Ph.D. thesis, Barcelona 1994
• Burgos Gil, J. I., Kramer, J., and Kühn, U.: Cohomological arithmetic Chow rings, J. Inst. Math. Jussieu 6\br(2007)\brr1–172
• Cartan, E.: Œvres complètes, Partie II, Volume I: Nombres complexes, Gauthier-Villars, 107–246
• Cartan, H. and Eilenberg, S.: Homological Algebra, Princeton Univ. Press, Princeton 1956
• Cassels, J. W. S.: Bounds for the least solutions of homogeneous quadratic equations, Proc. Cambridge Philos. Soc. 51\br(1955)\brr262–264
• Cassels, J. W. S.: Global fields, in: Algebraic number theory, Edited by J. W. S. Cassels and A. Fröhlich, Academic Press and Thompson Book Co., London and Washington 1967
• Cassels, J. W. S. and Guy, M. J. T.: On the Hasse principle for cubic surfaces, Mathematika 13\br(1966)\brr111–120.
• Chambert-Loir, A.: Points de petite hauteur sur les variétés semi-abéliennes, Ann. Sci. École Norm. Sup. 33\br(2000)\brr789–821
• Chambert-Loir, A. and Tschinkel, Y.: On the distribution of points of bounded height on equivariant compactifications of vector groups, Invent. Math. 148\br(2002)\brr421–452
• Chase, S. U.: Two remarks on central simple algebras, Comm. in Algebra 12\br(1984)\brr2279–2289
• Châtelet, F.: Variations sur un thème de H. Poincaré, Annales E. N. S. 61\br(1944)\brr249–300
• Châtelet, F.: Géométrie diophantienne et théorie des algèbres, Séminaire Dubreil, 1954–55, exposé 17
• Clemens, C. H. and Griffiths, P. A.: The intermediate Jacobian of the cubic threefold, Annals of Math. 95\br(1972)\brr281–356
• Cohen, H.: A course in computational algebraic number theory, Graduate Texts in Mathematics 138, Springer, Berlin, Heidelberg 1993
• Cohen, H.: Advanced topics in computational number theory, Graduate Texts in Mathematics 193, Springer, New York 2000
• Colliot-Thélène, J.-L.: Hilbert’s theorem 90 for $K_{2}$, with application to the Chow group of rational surfaces, Invent. Math. 35\br(1983)\brr1–20
• Colliot-Thélène, J.-L.: Les grands thèmes de François Châtelet, L’Enseignement Mathématique 34\br(1988)\brr387–405
• Colliot-Thélène, J.-L.: Cycles algébriques de torsion et $K$-théorie algébrique, in: Arithmetic Algebraic Geometry (Trento 1991), Lecture Notes Math. 1553, Springer, Berlin, Heidelberg 1993, 1–49
• Colliot-Thélène, J.-L., Kanevsky, D., and Sansuc, J.-J.: Arithmétique des surfaces cubiques diagonales, in: Diophantine approximation and transcendence theory (Bonn 1985), Lecture Notes in Math. 1290, Springer, Berlin 1987, 1–108
• Colliot-Thélène, J.-L. and Sansuc, J.-J.: Torseurs sous des groupes de type multiplicatif, applications à l’étude des points rationnels de certaines variétés algébriques, C. R. Acad. Sci. Paris Sér I Math. 282\br(1976)\brr1113–1116
• Colliot-Thélène, J.-L. and Sansuc, J.-J.: On the Chow groups of certain rational surfaces: A sequel to a paper of S. Bloch, Duke Math. J. 48\br(1981)\brr421–447
• Colliot-Thélène, J.-L. and Sansuc, J.-J.: La descente sur les variétés rationnelles II, Duke Math. J. 54\br(1987)\brr375–492
• Colliot-Thélène, J.-L. and Skorobogatov, A. N.: Good reduction of the Brauer-Manin obstruction, Trans. Amer. Math. Soc. 365\br(2013)\brr579–590
• Colliot-Thélène, J.-L. and Swinnerton-Dyer, Sir Peter: Hasse principle and weak approximation for pencils of Severi-Brauer and similar varieties, J. für die Reine und Angew. Math. 453\br(1994)\brr49–112
• Cormen, T., Leiserson, C., and Rivest, R.: Introduction to algorithms, MIT Press and McGraw-Hill, Cambridge and New York 1990
• Corn, P. K.: Del Pezzo surfaces and the Brauer-Manin obstruction, Ph.D. thesis, Harvard 2005
• Cornell, G. and Silverman, J. H.: Arithmetic geometry, Papers from the conference held at the University of Connecticut, Springer, New York 1986
• Cox, D. A.: The homogeneous coordinate ring of a toric variety, J. Algebraic Geom. 4\br(1995)\brr17–50
• de la Bretèche, R.: Sur le nombre de points de hauteur bornée d’une certaine surface cubique singulière, Astérisque 251\br(1998)\brr51–77
• de la Bretèche, R.: Compter des points d’une variété torique, J. Number Theory 87\br(2001)\brr315–331
• de la Bretèche, R.: Nombre de points de hauteur bornée sur les surfaces de del Pezzo de degré 5, Duke Math. J. 113\br(2002)\brr421–464
• de la Bretèche, R.: Répartition de points rationnels sur la cubique de Segre, Proc. London Math. Soc. 95\br(2007)\brr69–155
• de la Bretèche, R. and Browning, T. D.: On Manin’s conjecture for singular del Pezzo surfaces of degree $4$ I, Michigan Math. J. 55\br(2007)\brr51–80
• de la Bretèche, R. and Browning, T. D.: On Manin’s conjecture for singular del Pezzo surfaces of degree four II, Math. Proc. Cambridge Philos. Soc. 143\br(2007)\brr579–605
• de la Bretèche, R. and Browning, T. D.: Manin’s conjecture for quartic del Pezzo surfaces with a conic fibration, Duke Math. J. 160\br(2011)\brr1–69
• de la Bretèche, R., Browning, T. D., and Derenthal, U.: On Manin’s conjecture for a certain singular cubic surface, Ann. Sci. École Norm. Sup. 40\br(2007)\brr1–50
• de la Bretèche, R., Browning, T. D., and Peyre, E.: On Manin’s conjecture for a family of Châtelet surfaces, Annals of Math. 175\br(2012)\brr297–343
• de la Bretèche, R. and Swinnerton-Dyer, Sir Peter: Fonction zêta des hauteurs associée à une certaine surface cubique, Bull. Soc. Math. France 135\br(2007)\brr65–92
• Deligne, P.: La conjecture de Weil I, Publ. Math. IHES 43\br(1974)\brr273–307
• Derenthal, U.: Geometry of universal torsors, Ph.D. thesis, Göttingen 2006
• Derenthal, U., Elsenhans, A.-S., and Jahnel, J.: On Peyre’s constant alpha for del Pezzo surfaces, Math. Comp. 83\br(2014)\brr965–977
• Derenthal, U. and Janda, F.: Gaussian rational points on a singular cubic surface, arXiv:1105.2807
• Derenthal, U. and Tschinkel, Y.: Universal torsors over del Pezzo surfaces and rational points, in: Equidistribution in number theory, an introduction, Springer, Dordrecht 2007, 169–196
• Deuring, M.: Algebren, Springer, Ergebnisse der Math. und ihrer Grenzgebiete, Berlin 1935
• Dickson, L. E.: Determination of all the subgroups of the known simple group of order $25\,920$, Trans. Amer. Math. Soc. 5\br(1904)\brr126–166
• Dickson, L. E.: On finite algebras, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Math.-Phys. Klasse, 1905, 358–393
• Dieudonné, J.: Foundations of modern analysis, Pure and Applied Mathematics, Volume 10-I, Academic Press, New York, London 1969
• Dieudonné, J.: Treatise on analysis, Volume II, Translated from the French by I. G. MacDonald, Enlarged and corrected printing, Pure and Applied Mathematics, Volume 10-II, Academic Press, New York, London 1976
• Dieudonné, J.: Treatise on analysis, Volume III, Translated from the French by I. G. MacDonald, Pure and Applied Mathematics, Volume 10-III, Academic Press, New York, London 1972
• Dokchitser, T.: Computing special values of motivic $L$-functions, Experiment. Math. 13\br(2004)\brr137–149
• Dolgachev, I. V.: Classical Algebraic Geometry: a modern view, Cambridge University Press, Cambridge 2012
• Draxl, P. K.: Skew fields, London Math. Soc. Lecture Notes Series 81, Cambridge University Press, Cambridge 1983
• Duke, W.: Extreme values of Artin $L$-functions and class numbers, Compositio Math. 136\br(2003)\brr103–115
• Edidin, D., Hassett, B., Kresch, A., and Vistoli, A.: Brauer groups and quotient stacks, Amer. J. Math. 123\br(2001)\brr761–777
• Ekedahl, T.: An effective version of Hilbert’s irreducibility theorem, in: Séminaire de Théorie des Nombres, Paris 1988–1989, Progr. Math. 91, Birkhäuser, Boston 1990, 241–249
• Grothendieck, A. et Dieudonné, J.: Éléments de Géométrie Algébrique, Publ. Math. IHES 4, 8, 11, 17, 20, 24, 28, 32\br(1960–68)
• Elkies, N. D.: Rational points near curves and small nonzero $|x^3 - y^2|$ via lattice reduction, in: Algorithmic number theory (Leiden 2000), Lecture Notes in Computer Science 1838, Springer, Berlin 2000, 33–63
• Elsenhans, A.-S. and Jahnel, J.: The Fibonacci sequence modulo $p^2$—An investigation by computer for $p < 10^{14}$, Preprint
• Elsenhans, A.-S. and Jahnel, J.: The Diophantine equation $x^ 4 + 2 y^ 4 = z^ 4 + 4 w^ 4$, Math. Comp. 75\br(2006)\brr935–940
• Elsenhans, A.-S. and Jahnel, J.: The Diophantine equation $x^ 4 + 2 y^ 4 = z^ 4 + 4 w^ 4$ — a number of improvements, Preprint
• Elsenhans, A.-S. and Jahnel, J.: The asymptotics of points of bounded height on diagonal cubic and quartic threefolds, in: Algorithmic number theory, Lecture Notes in Computer Science 4076, Springer, Berlin 2006, 317–332
• Elsenhans, A.-S. and Jahnel, J.: On the smallest point on a diagonal quartic threefold, J. Ramanujan Math. Soc. 22\br(2007)\brr189–204
• Elsenhans, A.-S. and Jahnel, J.: Experiments with general cubic surfaces, in: Tschinkel, Y. and Zarhin, Y. (Eds.): Algebra, Arithmetic, and Geometry, In Honor of Yu. I. Manin, Volume I, Progress in Mathematics 269, Birkhäuser, Boston 2007, 637–654
• Elsenhans, A.-S. and Jahnel, J.: On the smallest point on a diagonal cubic surface, Experimental Mathematics 19\br(2010)\brr181–193
• Elsenhans, A.-S. and Jahnel, J.: New sums of three cubes, Math. Comp. 78\br(2009)\brr1227–1230
• Elsenhans, A.-S. and Jahnel, J.: List of solutions of $x^3 + y^3 + z^3 = n$ for 𝑛<1 000 neither a cube nor twice a cube, Web page available at the URL: http://\discretionary{}www.uni-math.gwdg.de\discretionary{/}/jahnel\discretionary{/}/Arbeiten\discretionary{/}/Liste\discretionary{/}/threecubes_20070419.txt
• Elsenhans, A.-S. and Jahnel, J.: On the Brauer-Manin obstruction for cubic surfaces, Journal of Combinatorics and Number Theory 2\br(2010)\brr107–128
• Faltings, G.: Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73\br(1983)\brr349–366
• Faltings, G.: Calculus on arithmetic surfaces, Annals of Math. 119\br(1984)\brr387–424
• Faltings, G.: The general case of S. Lang’s conjecture, in: Barsotti Symposium in Algebraic Geometry (Abano Terme 1991), Perspect. Math. 15, Academic Press, San Diego 1994, 175–182
• Faltings, G.: Lectures on the arithmetic Riemann-Roch theorem, Annals of Mathematics Studies 127, Princeton University Press, Princeton 1992
• Fincke, U. and Pohst, M.: Improved methods for calculating vectors of short length in a lattice, including a complexity analysis, Math. Comp. 44\br(1985)\brr463–471
• Forster, O.: Algorithmische Zahlentheorie, Vieweg, Braunschweig 1996
• Fouvry, È.: Sur la hauteur des points d’une certaine surface cubique singulière, Astérisque 251\br(1998)\brr31–49
• Franke, J., Manin, Yu. I., and Tschinkel, Y.: Rational points of bounded height on Fano varieties, Invent. Math. 95\br(1989)\brr421–435
• Frei, C.: Counting rational points over number fields on a singular cubic surface, arXiv:1204.0383
• Fulton, W.: Intersection theory, Springer, Ergebnisse der Math. und ihrer Grenzgebiete, 3. Folge, Band 2, Berlin 1984
• Gabber, O.: Some theorems on Azumaya algebras, in: The Brauer group (Les Plans-sur-Bex 1980), Lecture Notes Math. 844, Springer, Berlin, Heidelberg, New York 1981, 129–209
• Gatsinzi, J.-B. and Tignol, J.-P.: Involutions and Brauer-Severi varieties, Indag. Math. 7\br(1996)\brr149–160
• Gelbart, S. S.: Automorphic forms on adéle groups, Annals of Mathematics Studies 83, Princeton University Press, Princeton 1975
• Gillet, H., Soulé, C.: Arithmetic intersection theory, Publ. Math. IHES 72\br(1990)\brr93-174
• Gillet, H., Soulé, C.: An arithmetic Riemann-Roch theorem, Invent. Math. 110\br(1992)\brr473–543
• Giraud, J.: Cohomologie non abélienne, Springer, Grundlehren der math. Wissenschaften 179, Berlin, Heidelberg, New York 1971
• Griffiths, P. and Harris, J.: Principles of algebraic geometry, John Wiley & Sons, New York 1978
• Grothendieck, A.: Le groupe de Brauer, I: Algèbres d’Azumaya et interprétations diverses, Séminaire Bourbaki, 17$^\textrm {e}$ année 1964/65, n$^\textrm {o}$ 290
• Grothendieck, A.: Le groupe de Brauer, II: Théorie cohomologique, Séminaire Bourbaki, 18$^\textrm {e}$ année 1965/66, n$^\textrm {o}$ 297
• Grothendieck, A.: Le groupe de Brauer, III: Exemples et compléments, in: Grothendieck, A.: Dix exposés sur la Cohomologie des schémas, North-Holland, Amsterdam and Masson, Paris 1968, 88–188
• Gruenberg, K.: Profinite groups, in: Algebraic number theory, Edited by J. W. S. Cassels and A. Fröhlich, Academic Press and Thompson Book Co., London and Washington 1967
• Haberland, K.: Galois cohomology of algebraic number fields, With two appendices by H. Koch and Th. Zink, VEB Deutscher Verlag der Wissenschaften, Berlin 1978
• Haile, D. E.: On central simple algebras of given exponent, J. of Algebra 57\br(1979)\brr449–465
• Handbook of numerical analysis, edited by P. G. Ciarlet and J. L. Lions, Vols. II–IV, North-Holland Publishing Co., Amsterdam 1991–1996
• Harari, D.: Méthode des fibrations et obstruction de Manin, Duke Math. J. 75\br(1994)\brr221–260
• Harari, D.: Obstructions de Manin transcendantes, in: Number theory (Paris 1993–1994), London Math. Soc. Lecture Note Ser. 235, Cambridge Univ. Press, Cambridge 1996, 75–87
• Hardy, G. H. and Wright, E. M.: An introduction to the theory of numbers, Fifth edition, Oxford University Press, New York 1979
• Hartshorne, R.: Ample subvarieties of algebraic varieties, Lecture Notes Math. 156, Springer, Berlin-New York 1970
• Hartshorne, R.: Algebraic Geometry, Graduate Texts in Mathematics 52, Springer, New York 1977
• Hassett, B. and Várilly-Alvarado, A.: Failure of the Hasse principle on general $K3$ surfaces, arXiv:1110.1738
• Hassett, B., Várilly-Alvarado, A., and Varilly, P.: Transcendental obstructions to weak approximation on general $K3$ surfaces, Adv. Math. 228\br(2011)\brr1377–1404
• Heath-Brown, D. R.: The density of zeros of forms for which weak approximation fails, Math. Comp. 59\br(1992)\brr613–623
• Heath-Brown, D. R.: Zero-free regions for Dirichlet $L$-functions, and the least prime in an arithmetic progression, Proc. London Math. Soc. 64\br(1992)\brr265–338
• Heath-Brown, D. R.: The density of rational points on Cayley’s cubic surface, Bonner Math. Schriften 360\br(2003)\brr1–33
• Heath-Brown, D. R., Lioen, W. M., and te Riele, H. J. J.: On solving the diophantine equation $x^3 + y^3 +z^3 = k$ on a vector computer, Math. Comp. 61\br(1993)\brr235–244
• Heath-Brown, D. R. and Moroz, B. Z.: The density of rational points on the cubic surface $X_0^3 = X_1X_2X_3$, Math. Proc. Cambridge Philos. Soc. 125\br(1999)\brr385–395
• Heilbronn, H.: Zeta-functions and $L$-functions, in: Algebraic number theory, Edited by J. W. S. Cassels and A. Fröhlich, Academic Press and Thompson Book Co., London and Washington 1967
• Hennessy, J. L. and Patterson, D. A.: Computer Architecture: A Quantitative Approach, 2$^\textrm {nd}$ ed., Morgan Kaufmann, San Mateo (CA) 1996
• Henningsen, F.: Brauer-Severi-Varietäten und Normrelationen von Symbolalgebren, Doktorarbeit (Ph. D. thesis), available in electronic form at http://www.\discretionary{}biblio.\discretionary{}tu-bs.de/ediss/ data/20000713a/20000713a.pdf
• Hermann, G.: Die Frage der endlich vielen Schritte in der Theorie der Polynomideale, Math. Ann. 95\br(1926)\brr736–788
• Herstein, I. N.: Noncommutative rings, The Math. Association of America (Inc.), distributed by John Wiley and Sons, Menasha, WI 1968
• Heuser, A.: Über den Funktionenkörper der Normfläche einer zentral einfachen Algebra, J. für die Reine und Angew. Math. 301\br(1978)\brr105–113
• Hirzebruch, F.: Der Satz von Riemann-Roch in Faisceau-theoretischer Formulierung: Einige Anwendungen und offene Fragen, Proc. Int. Cong. of Mathematicians, Amsterdam 1954, vol. III, 457–473, Erven P. Noordhoff N.V. and North-Holland Publishing Co., Groningen and Amsterdam 1956
• Hoffman, J. W. and Weintraub, S. H.: Four dimensional symplectic geometry over the field with three elements and a moduli space of abelian surfaces, Note Mat. 20\br(2000/01)\brr111–157
• Hoffmann, N., Jahnel, J., and Stuhler, U.: Generalized vector bundles on curves, J. für die Reine und Angew. Math. 495\br(1998)\brr35-60
• Hoobler, R. T.: A cohomological interpretation of Brauer groups of rings, Pacific J. Math. 86\br(1980)\brr89–92
• Ieronymou, E.: Diagonal quartic surfaces and transcendental elements of the Brauer groups, J. Inst. Math. Jussieu 9\br(2010)\brr769–798
• Ieronymou, E., Skorobogatov, A., and Zarhin, Yu.: On the Brauer group of diagonal quartic surfaces, With an appendix by Peter Swinnerton-Dyer, J. Lond. Math. Soc. 83\br(2011)\brr659–672
• Ireland, K. F. and Rosen, M. I.: A classical introduction to modern number theory, Graduate Texts in Mathematics 84, Springer, New York and Berlin 1982
• \textcyr{Iskovskih, V. A.: Kontrprimer k principu Khasse dlya sistemy dvukh kvadratichnykh form ot pyati peremennykh, Matematicheskie Zametki 10\br(1971)\brr253–257} English translation: Iskovskih, V. A.: A counterexample to the Hasse principle for systems of two quadratic forms in five variables, Mathematical Notes 10\br(1971)\brr575–577
• Jacobson, N.: Structure of rings, Revised edition, Amer. Math. Soc. Coll. Publ. 37, Amer. Math. Soc., Providence, R.I. 1964
• Jahnel, J.: Line bundles on arithmetic surfaces and intersection theory, Manuscripta Math. 91\br(1996)\brr103–119
• Jahnel, J.: Heights for line bundles on arithmetic varieties, Manuscripta Math. 96\br(1998)\brr421–442
• Jahnel, J.: A height function on the Picard group of singular Arakelov varieties, in: Algebraic K-Theory and Its Applications, Proceedings of the Workshop and Symposium held at ICTP Trieste, September 1997, edited by H. Bass, A. O. Kuku and C. Pedrini, World Scientific, Singapore 1999, 410–436
• Jahnel, J.: The Brauer-Severi variety associated with a central simple algebra, Linear Algebraic Groups and Related Structures 52\br(2000)\brr1–60
• Jahnel, J.: More cubic surfaces violating the Hasse principle, Journal de Théorie des Nombres de Bordeaux 23\br(2011)\brr471–477
• Jahnel, J.: On the distribution of small points on abelian and toric varieties, Preprint
• de Jong, A. J.: Smoothness, semi-stability and alterations, Publ. Math. IHES 83\br(1996)\brr51–93
• de Jong, A. J.: A result of Gabber, Preprint, available at the URL: http://www.math\discretionary{.}.columbia.edu\discretionary{/}/~dejong/papers/2-gabber.pdf
• Kempf, G., Knudsen, F. F., Mumford, D., and Saint-Donat, B.: Toroidal embeddings I, Lecture Notes in Mathematics 339, Springer, Berlin-New York 1973
• Kersten, I.: Brauergruppen von Körpern, Vieweg, Braunschweig 1990
• Kersten, I. and Rehmann, U.: Generic splitting of reductive groups, Tôhoku Math. J. 46\br(1994)\brr35–70
• Knus, M. A. and Ojanguren, M.: Théorie de la descente et algèbres d’Azumaya, Springer, Lecture Notes Math. 389, Berlin, Heidelberg, New York 1974
• Knus, M. A. and Ojanguren, M.: Cohomologie étale et groupe de Brauer, in: The Brauer group (Les Plans-sur-Bex 1980), Lecture Notes Math. 844, Springer, Berlin, Heidelberg, New York 1981, 210–228
• Kresch, A. and Tschinkel, Y.: Effectivity of Brauer-Manin obstructions, Preprint
• Kress, R.: Numerical analysis, Graduate Texts in Mathematics 181, Springer, New York 1998
• Laface, A. and Velasco, M.: A survey on Cox rings, Geom. Dedicata 139\br(2009)\brr269–287
• Lang, S.: Hyperbolic and Diophantine analysis, Bull. Amer. Math. Soc. 14\br(1986)\brr159–205
• Lang, S.: Algebra, Third Edition, Addison-Wesley, Reading, MA 1993
• \textcyr{Lavrik, A. F.: O funkcionalp1nykh uravneniyakh funkciĭ Dirikhle, Izv. Akad. Nauk SSSR, Ser. Mat. 31\br(1967)\brr431–442} English translation: Lavrik, A. F.: On functional equations of Dirichlet functions, Math. USSR-Izv. 31\br(1967)\brr421–432
• Lazarsfeld, R.: Positivity in algebraic geometry I, Ergebnisse der Mathematik und ihrer Grenzgebiete (3. Folge) 48, Springer, Berlin 2004
• Le Boudec, P.: Manin’s conjecture for a cubic surface with $2A_2+A_1$ singularity type, Math. Proc. Cambridge Philos. Soc. 153\br(2012)\brr419–455
• Le Boudec, P.: Manin’s conjecture for a quartic del Pezzo surface with $A_3$ singularity and four lines, Monatsh. Math. 167\br(2012)\brr481–502
• Le Boudec, P.: Manin’s conjecture for two quartic del Pezzo surfaces with $3A_1$ and $A_1+A_2$ singularity types, Acta Arith. 151\br(2012)\brr109–163
• Lelong, P.: Fonctions plurisousharmoniques et formes différentielles positives, Gordon & Breach, Paris 1968
• Lichtenbaum, S.: Duality theorems for curves over $p$-adic fields, Invent. Math. 7\br(1969)\brr120–136
• Lind, C.-E.: Untersuchungen über die rationalen Punkte der ebenen kubischen Kurven vom Geschlecht Eins, Doktorarbeit (Ph.D. thesis), Uppsala 1940
• Lorenz, F. and Opolka, H.: Einfache Algebren und projektive Darstellungen über Zahlkörpern, Math. Z. 162\br(1978)\brr175–182
• Loughran, D.: Manin’s conjecture for a singular sextic del Pezzo surface, Journal de Théorie des Nombres de Bordeaux 22\br(2010)\brr675–701
• Loughran, D.: Manin’s conjecture for a singular quartic del Pezzo surface, J. London Math. Soc. 86\br(2012)\brr558–584
• Lovász, L.: How to compute the volume?, Jahresbericht der DMV, Jubiläumstagung 100 Jahre DMV (Bremen 1990), 138–151
• Maclagan-Wedderburn, J. H.: A theorem on finite algebras, Trans. Amer. Math. Soc. 6\br(1905)\brr349–352
• Maclagan-Wedderburn, J. H.: On hypercomplex numbers, Proc. London Math. Soc., 2nd Series, 6\br(1908)\brr77–118
• \textcyr{Manin, Yu. I.: Kubicheskie formy: algebra, geometriya, arifmetika, Nauka, Moskva 1972} English translation: Manin, Yu. I.: Cubic forms, algebra, geometry, arithmetic, North-Holland Publishing Co. and American Elsevier Publishing Co., Amsterdam-London and New York 1974
• Marcus, D. A.: Number fields, Springer, New York - Heidelberg 1977
• Matsumura, H.: Commutative ring theory, Cambridge Studies in Advanced Mathematics 8, Cambridge University Press, Cambridge 1986
• McKinnon, D.: Counting rational points on $K3$ surfaces, J. Number Theory 84\br(2000)\brr49–62
• McKinnon, D.: Vojta’s conjecture implies the Batyrev-Manin conjecture for $K3$ surfaces, Bull. Lond. Math. Soc. 43\br(2011)\brr1111–1118
• O’Meara, O. T.: Introduction to quadratic forms, Springer, Berlin, New York 1963
• Merkurjev, A. S.: Brauer groups of fields, Comm. in Algebra 11\br(1983)\brr2611–2624
• \textcyr{Merkurp1ev, A. S.: O stroenii gruppy Braue1ra poleĭ, Izv. Akad. Nauk SSSR Ser. Mat. 49\br(1985)\brr828–846,} English translation: Merkurjev, A. S.: Structure of the Brauer group of fields, Math. USSR-Izv. 27\br(1986)\brr141–157
• \textcyr{Merkurp1ev, A. S.: Zamknutye tochki mnogoobraziĭ Severi-Braue1ra, Vestnik S.-Peterburg. Univ. Mat. Mekh. Astronom. 1993-2\br(1993)\brr51–53} English translation: Merkurjev, A. S.: Closed points of Brauer-Severi varieties, Vestnik St. Petersburg Univ. Math. 26-2\br(1993)\brr44–46
• \textcyr{Merkurp1ev, A. S. i Suslin, A. A.: $K$-kogomologii mnogoobraziĭ Severi-Braue1ra i gomomorfizm normennogo vycheta, Izv. Akad. Nauk SSSR Ser. Mat. 46\br(1982)\brr1011–1046,} English translation: Merkurjev, A. S. and Suslin, A. A.: $K$-cohomology of Severi-Brauer varieties and the norm residue homomorphism, Math. USSR-Izv. 21\br(1983)\brr307–340
• de Meyer, F. and Ford, T. J.: On the Brauer group of surfaces and subrings of $k[x,y]$, in: van Oystaeyen, F. and Verschoren, A. (Eds.): Brauer groups in ring theory and algebraic geometry, Proceedings of a conference held at Antwerp 1981, Lecture Notes Math. 917, Springer, Berlin, Heidelberg, New York 1982, 211–221
• de Meyer, F. and Ingraham, E.: Separable algebras over commutative rings, Lecture Notes Math. 181, Springer, Berlin, Heidelberg, New York 1971
• Milne, J. S.: Étale Cohomology, Princeton University Press, Princeton 1980
• Molien, T.: Über Systeme höherer complexer Zahlen, Math. Ann. 41\br(1893)\brr83–156
• Mordell, L. J.: On the conjecture for the rational points on a cubic surface, J. London Math. Soc. 40\br(1965)\brr149–158
• Morita, Y.: Remarks on a conjecture of Batyrev and Manin, Tohoku Math. J. 49\br(1997)\brr437–448
• Moriwaki, A.: Intersection pairing for arithmetic cycles with degenerate Green currents, E-print AG/9803054
• Murre, J. P.: Algebraic equivalence modulo rational equivalence on a cubic threefold, Compositio Math. 25\br(1972)\brr161–206
• Murty, M. R.: Applications of symmetric power $L$-functions, in: Lectures on automorphic $L$-functions, Fields Inst. Monogr. 20, Amer. Math. Soc., Providence 2004, 203–283
• Nakayama, T.: Divisionsalgebren über diskret bewerteten perfekten Körpern, J. für die Reine und Angew. Math. 178\br(1937)\brr11–13
• Nathanson, M. B.: Elementary methods in number theory, Graduate Texts in Mathematics 195, Springer, New York 2000
• Neukirch, J.: Algebraic number theory, Grundlehren der Mathematischen Wissenschaften 322, Springer, Berlin 1999
• Noether, M.: Rationale Ausführung der Operationen in der Theorie der algebraischen Funktionen, Math. Ann. 23\br(1884)\brr311–358
• Orzech, M.: Brauer Groups and Class Groups for a Krull Domain, in: van Oystaeyen, F. and Verschoren, A. (Eds.): Brauer groups in ring theory and algebraic geometry, Proceedings of a conference held at Antwerp 1981, Lecture Notes Math. 917, Springer, Berlin, Heidelberg, New York 1982, 66–90
• Orzech, M. and Small, C.: The Brauer group of commutative rings: Brauer-Manin obstruction, Lecture Notes in Pure and Applied Mathematics 11, Marcel Dekker, New York 1975
• Orzech, M. and Verschoren, A.: Some remarks on Brauer groups of Krull domains, in: van Oystaeyen, F. and Verschoren, A. (Eds.): Brauer groups in ring theory and algebraic geometry, Proceedings of a conference held at Antwerp 1981, Lecture Notes Math. 917, Springer, Berlin, Heidelberg, New York 1982, 91–95
• Peyre, E.: Hauteurs et mesures de Tamagawa sur les variétés de Fano, Duke Math. J. 79\br(1995)\brr101–218
• Peyre, E.: Products of Severi-Brauer varieties and Galois cohomology, in: Proc. Symp. Pure Math. 58, Part 2: $K$-theory and algebraic geometry: connections with quadratic forms and division algebras (Santa Barbara, CA 1992), Amer. Math. Soc., Providence, R.I. 1995, 369–401
• Peyre, E.: Points de hauteur bornée et géométrie des variétés (d’après Y. Manin et al.), Séminaire Bourbaki 2000/2001, Astérisque 282\br(2002)\brr323–344
• Peyre, E.: Points de hauteur bornée, topologie adélique et mesures de Tamagawa, Journal de Théorie des Nombres de Bordeaux 15\br(2003)\brr319–349
• Peyre, E. and Tschinkel, Y.: Tamagawa numbers of diagonal cubic surfaces, numerical evidence, Math. Comp. 70\br(2001)\brr367–387
• Pierce, R. S.: Associative Algebras, Graduate Texts in Mathematics 88, Springer, New York 1982
• Pohst, M. and Zassenhaus, H.: Algorithmic algebraic number theory, Encyclopedia of Mathematics and its Applications 30, Cambridge University Press, Cambridge 1989
• Poincaré, H.: Sur les propriétés arithmétiques des courbes algébriques, J. Math. Pures et Appl. 5$^{e}$ série, 7\br(1901)\brr161–234
• Poonen, B.: Insufficiency of the Brauer-Manin obstruction applied to éétale covers, Annals of Math. 171\br(2010)\brr2157–2169
• Poonen, B. and Tschinkel, Y. (eds.): Arithmetic of higher-dimensional algebraic varieties, Proceedings of the Workshop on Rational and Integral Points of Higher-Dimensional Varieties held in Palo Alto, CA, December 11–20, 2002, Birkhäuser, Progress in Mathematics 226, Boston 2004
• Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T.: Numerical recipes, The art of scientific computing, Cambridge University Press, Cambridge 1986
• Preu, T.: Transcendental Brauer-Manin Obstruction for a Diagonal Quartic Surface, Ph.D. thesis, Zürich 2010
• Quillen, D.: Higher algebraic $K$-theory I, in: Algebraic $K$-theory I, Higher $K$-theories, Lecture Notes Math. 341, Springer, Berlin, Heidelberg, New York 1973, 85–147
• Reiner, I.: Maximal orders, Academic Press, London-New York 1975
• Robbiani, M.: On the number of rational points of bounded height on smooth bilinear hypersurfaces in biprojective space, J. London Math. Soc. 63\br(2001)\brr33–51
• Roquette, P.: On the Galois cohomology of the projective linear group and its applications to the construction of generic splitting fields of algebras, Math. Ann. 150\br(1963)\brr411–439
• Roquette, P.: Isomorphisms of generic splitting fields of simple algebras, J. für die Reine und Angew. Math. 214/215\br(1964)\brr207–226
• Roux, B.: Sur le groupe de Brauer d’un corps local à corps résiduel imparfait, in: Groupe d’Etude d’Analyse Ultramétriuqe, Publ. Math. de l’Univ. de Paris VII 29\br(1985/86)\brr85–97
• Salberger, P.: Tamagawa measures on universal torsors and points of bounded height on Fano varieties, Astérisque 251\br(1998)\brr91–258
• Saltman, P. J.: Division algebras over discrete valued fields, Comm. in Algebra 8\br(1980)\brr1749–1774
• Saltman, P. J.: The Brauer group is torsion, Proc. Amer. Math. Soc. 81\br(1981)\brr385–387
• Satake, I.: On the structure of Brauer group of a discretely valued complete field, Sci. Papers Coll. Gen. Ed. Univ. Tokyo 1\br(1951)\brr1–10
• Schanuel, S.: On heights in number fields, Bull. Amer. Math. Soc. 70\br(1964)\brr262–263
• Scharlau, W.: Quadratic and Hermitian forms, Springer, Grundlehren der Math. Wissenschaften 270, Berlin, Heidelberg, New York 1985
• Schindler, D.: On Diophantine equations involving norm forms and bihomogenous forms, Ph.D. thesis, Bristol 2013
• Schindler, D.: Manin’s conjecture for certain biprojective hypersurfaces, arXiv:\discretionary{}1307.\discretionary{}7069
• Schmidt, W. M.: The density of integer points on homogeneous varieties, Acta Math. 154\br(1985)\brr243–296
• Schönhage, A. and Strassen, V.: Schnelle Multiplikation großer Zahlen, Computing 7\br(1971)\brr281–292
• Schröer, S.: There are enough Azumaya algebras on surfaces, Math. Ann. 321\br(2001)\brr439–454
• Schwarz, H. A.: Sur une définition erronée de l’aire d’une surface courbe, Communication faite à M. Charles Hermite, 1881–82, in: Gesammelte Mathematische Abhandlungen, Zweiter Band, Springer, Berlin 1890, 309–311
• Sedgewick, R.: Algorithms, Addison-Wesley, Reading 1983
• Seelinger, G.: A description of the Brauer-Severi scheme of trace rings of generic matrices, J. of Algebra 184\br(1996)\brr852–880
• Seelinger, G.: Brauer-Severi schemes of finitely generated algebras, Israel J. Math. 111\br(1999)\brr321–337
• Selmer, E. S.: The Diophantine equation $ax^ 3+by^ 3+cz^ 3=0$, Acta Math. 85\br(1951)\brr203–362
• Serre, J.-P.: Corps locaux, Hermann, Paris 1962
• Serre, J.-P.: Local class field theory, in: Algebraic number theory, Edited by J. W. S. Cassels and A. Fröhlich, Academic Press and Thompson Book Co., London and Washington 1967
• Serre, J.-P.: Propriétés galoisiennes des points d’ordre fini des courbes elliptiques, Invent. Math. 15\br(1972)\brr259–331
• Serre, J.-P.: Cohomologie Galoisienne, Lecture Notes in Mathematics 5, Quatrième Edition, Springer, Berlin 1973
• Severi, F.: Un nuovo campo di richerche nella geometria sopra una superficie e sopra una varietà algebrica, Mem. della Acc. R. d’Italia 3\br(1932)\brr1–52 = Opere matematiche, vol. terzo, Acc. Naz. Lincei, Roma, 541–586
• Demazure, A. et Grothendieck, A.: Schemas en groupes, Séminaire de Géométrie Algébrique du Bois Marie 1962–64 (SGA 3), Lecture Notes Math. 151, 152, 153, Springer, Berlin, Heidelberg, New York 1970
• Artin, M., Grothendieck, A. et Verdier, J.-L. (avec la collaboration de Deligne, P. et Saint-Donat, B.): Théorie des topos et cohomologie étale des schémas, Séminaire de Géométrie Algébrique du Bois Marie 1963–1964 (SGA 4), Lecture Notes in Math. 269, 270, 305, Springer, Berlin, Heidelberg, New York 1973
• Deligne, P. (avec la collaboration de Boutot, J. F., Grothendieck, A., Illusie, L. et Verdier, J. L.): Cohomologie Étale, Séminaire de Géométrie Algébrique du Bois Marie (SGA 4$\frac {1}{2}$), Lecture Notes Math. 569, Springer, Berlin, Heidelberg, New York 1977
• Berthelot, P., Grothendieck, A. et Illusie, L. (Avec la collaboration de Ferrand, D., Jouanolou, J. P., Jussila, O., Kleiman, S., Raynaud, M. et Serre, J. P.): Théorie des intersections et théorème de Riemann-Roch, Séminaire de Géométrie Algébrique du Bois Marie 1966-67 (SGA 6), Lecture Notes in Math. 225, Springer, Berlin-New York 1971
• Siegel, C. L.: Analytische Zahlentheorie, Teil II, Vorlesung, ausgearbeitet von K. F. Kürten und G. Köhler, Universität Göttingen 1963/64
• Siegel, C. L.: Abschätzung von Einheiten, Nachr. Akad. Wiss. Göttingen, Math.-Phys. Kl. II 1969\br(1969)\brr71–86
• Siegel, C. L.: Normen algebraischer Zahlen, Nachr. Akad. Wiss. Göttingen, Math.-Phys. Kl. II 1973\br(1973)\brr197–215
• Sims, C. C.: Computational methods in the study of permutation groups, in: Computational Problems in Abstract Algebra (Proc. Conf., Oxford 1967), Pergamon, Oxford 1970, 169–183
• Skorobogatov, A.: Torsors and rational points, Cambridge Tracts in Mathematics 144, Cambridge University Press, Cambridge 2001
• Skorobogatov, A. N. and Zarhin, Yu. G.: The Brauer group of Kummer surfaces and torsion of elliptic curves, J. Reine Angew. Math. 666\br(2012)\brr115–140
• Skorobogatov, A. and Swinnerton-Dyer, Sir Peter: $2$-descent on elliptic curves and rational points on certain Kummer surfaces, Adv. Math. 198\br(2005)\brr448–483
• Slater, J. B. and Swinnerton-Dyer, Sir Peter: Counting points on cubic surfaces I, in: Nombre et répartition de points de hauteur bornée (Paris 1996), Astérisque 251\br(1998)\brr1–12
• Smart, N. P.: The algorithmic resolution of Diophantine equations, London Mathematical Society Student Texts 41, Cambridge University Press, Cambridge 1998
• Soulé, C., Abramovich, D., Burnol, J.-F., and Kramer, J.: Lectures on Arakelov geometry, Cambridge Studies in Advanced Mathematics 8, Cambridge University Press, Cambridge 1992
• Spanier, E. H.: Algebraic topology, McGraw-Hill, New York-Toronto-London 1966
• Stark, H. M.: Some effective cases of the Brauer-Siegel theorem, Invent. Math. 23\br(1974)\brr135–152
• Stark, H. M.: Class fields for real quadratic fields and $L$-series at $1$, in: Algebraic number fields: $L$-functions and Galois properties (Proc. Sympos., Durham, 1975), Academic Press, London 1977, 355–375
• Strauch, M. and Tschinkel, Y.: Height zeta functions of twisted products, Math. Res. Lett. 4\br(1997)\brr273–282
• \textcyr{Suslin, A. A.: Kvaternionnyĭ gomomorfizm dlya polya funktsiĭ na konike, Dokl. Akad. Nauk SSSR 265\br(1982)\brr292–296,} English translation: Suslin, A. A.: The quaternion homomorphism for the function field on a conic, Soviet Math. Dokl. 26\br(1982)\brr72–77
• Swiȩcicka, J.: Small deformations of Brauer-Severi schemes, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26\br(1978)\brr591–593
• Swinnerton-Dyer, Sir Peter: Two special cubic surfaces, Mathematika 9\br(1962)\brr54–56
• Swinnerton-Dyer, Sir Peter: The Brauer group of cubic surfaces, Math. Proc. Cambridge Philos. Soc. 113\br(1993)\brr449–460
• Swinnerton-Dyer, Sir Peter: Rational points on fibered surfaces, in: Tschinkel, Y. (ed.): Mathematisches Institut, Seminars 2004, Universitätsverlag, Göttingen 2004, 103–109
• Swinnerton-Dyer, Sir Peter: Counting points on cubic surfaces II, in: Geometric methods in algebra and number theory, Progr. Math. 235, Birkhäuser, Boston 2005, 303–309
• Szeto, G.: Splitting Rings for Azumaya Quaternion Algebras, in: van Oystaeyen, F. and Verschoren, A. (Eds.): Brauer groups in ring theory and algebraic geometry, Proceedings of a conference held at Antwerp 1981, Lecture Notes Math. 917, Springer, Berlin, Heidelberg, New York 1982, 118–125
• Szpiro, L.: Sur les propriétés numériques du dualisant relatif d’une surface arithmétique, The Grothendieck Festschrift, vol. III, Birkhäuser, Boston 1990
• Szpiro, L., Ullmo, E., Zhang, S.: Equirépartition des petits points, Invent. Math. 127\br(1997)\brr337-347
• Tate, J.: Global class field theory, in: Algebraic number theory, Edited by J. W. S. Cassels and A. Fröhlich, Academic Press and Thompson Book Co., London and Washington 1967
• Tate, J.: Algorithm for determining the type of a singular fiber in an elliptic pencil, Modular functions of one variable IV (Proc. Internat. Summer School, Antwerp 1972), Lecture Notes in Math. 476, Springer, Berlin 1975, 33–52
• Tignol, J.-P.: Sur les decompositions des algèbres à divisions en produit tensoriel d’algèbres cycliques, in: van Oystaeyen, F. and Verschoren, A. (Eds.): Brauer groups in ring theory and algebraic geometry, Proceedings of a conference held at Antwerp 1981, Lecture Notes Math. 917, Springer, Berlin, Heidelberg, New York 1982, 126–145
• Tignol, J.-P.: On the corestriction of central simple algebras, Math. Z. 194\br(1987)\brr267–274
• \textcyr{Tregub, S. L.: O biratsionalp1noĭ e1kvivalentnosti mnogoobraziĭ Braue1ra-Severi, Uspekhi Mat. Nauk 46-6\br(282)\br(1991)\brr217–218} English translation: Tregub, S. L.: On the birational equivalence of Brauer-Severi varieties, Russian Math. Surveys 46-6\br(1991)\brr229
• Turner, S.: The zeta function of a birational Severi-Brauer scheme, Bol. Soc. Brasil. Mat. 10\br(1979)\brr25–50
• Ullmo, E.: Positivité et discrétion des points algébriques des courbes, Annals of Math. 147\br(1998)\brr167-179
• Vaughan, R. C.: The Hardy-Littlewood method, Cambridge Tracts in Mathematics 80, Cambridge University Press, Cambridge 1981
• Verschoren, A.: A check list on Brauer groups, in: van Oystaeyen, F. and Verschoren, A. (Eds.): Brauer groups in ring theory and algebraic geometry, Proceedings of a conference held at Antwerp 1981, Lecture Notes Math. 917, Springer, Berlin, Heidelberg, New York 1982, 279–300
• Wang, S.: On the commutator group of a simple algebra, Amer. J. Math. 72\br(1950)\brr323–334
• Warner, F. W.: Foundations of differentiable manifolds and Lie groups, Scott, Foresman and Co., Glenview-London 1971
• Weil, A.: Sur les courbes algébriques et les variétés qui s’en déduisent, Actualités Sci. Ind. 1041, Hermann et Cie., Paris 1948
• Weil, A.: The field of definition of a variety, Amer. J. of Math. 78\br(1956)\brr509–524
• Weyl, H.: Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77\br(1916)\brr313–352
• Witt, E.: Über ein Gegenbeispiel zum Normensatz, Math. Z. 39\br(1935)\brr462–467
• Witt, E.: Schiefkörper über diskret bewerteten Körpern, J. für die Reine und Angew. Math. 176\br(1937)\brr153–156
• Wittenberg, O.: Transcendental Brauer-Manin obstruction on a pencil of elliptic curves, in: Arithmetic of higher-dimensional algebraic varieties (Palo Alto 2002), Progr. Math. 226, Birkhäuser, Boston 2004, 259–267
• \textcyr{Yanchevskiĭ, V. I.: Printsip Khasse dlya grupp Braue1ra poleĭ funktsiĭ na proizveeniyakh mnogoobraziĭ Severi-Braue1ra i proektivnykh kvadrik, Trudy Mat. Inst. imeni Steklova 208\br(1995)\brr350–365}
• Yuan, S.: On the Brauer groups of local fields, Annals of Math. 82\br(1965)\brr434–444
• Zak, F. L.: Tangents and secants of algebraic varieties, AMS Translations of Mathematical Monographs 127, Amer. Math. Soc., Providence 1993
• Zhang, S.: Small points and adelic metrics, J. Alg. Geom. 4\br(1995)\brr281-300
• Zhang, S.: Positive line bundles on arithmetic varieties, J. Amer. Math. Soc. 8\br(1995)\brr187-221
• Zhang, S.: Equidistribution of small points on abelian varieties, Annals of Math. 147\br(1998)\brr159-165