Intersection numbers of special cycles

Rohlfs, Jürgen; Schwermer, Joachim

doi:10.1090/S0894-0347-1993-1186963-2

Intersection numbers of special cycles
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by Jürgen Rohlfs and Joachim Schwermer

J. Amer. Math. Soc. 6 (1993), 755-778

DOI: https://doi.org/10.1090/S0894-0347-1993-1186963-2

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References

Armand Borel, Introduction aux groupes arithmétiques, Publications de l’Institut de Mathématique de l’Université de Strasbourg, XV. Actualités Scientifiques et Industrielles, No. 1341, Hermann, Paris, 1969 (French). MR 0244260
A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces. I, Amer. J. Math. 80 (1958), 458–538. MR 102800, DOI 10.2307/2372795
A. Borel and J.-P. Serre, Théorèmes de finitude en cohomologie galoisienne, Comment. Math. Helv. 39 (1964), 111–164 (French). MR 181643, DOI 10.1007/BF02566948
Armand Borel and Jacques Tits, Groupes réductifs, Inst. Hautes Études Sci. Publ. Math. 27 (1965), 55–150 (French). MR 207712

Compléments à l’article: ‘Groupes réductifs’

41

Theory of Lie groups

William Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 2, Springer-Verlag, Berlin, 1984. MR 732620, DOI 10.1007/978-3-662-02421-8
Werner Greub, Stephen Halperin, and Ray Vanstone, Connections, curvature, and cohomology, Pure and Applied Mathematics, Vol. 47-III, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Volume III: Cohomology of principal bundles and homogeneous spaces. MR 0400275
G. Harder, A Gauss-Bonnet formula for discrete arithmetically defined groups, Ann. Sci. École Norm. Sup. (4) 4 (1971), 409–455. MR 309145
Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
Friedrich Hirzebruch, Automorphe Formen und der Satz von Riemann-Roch, Symposium internacional de topología algebraica International symposium on algebraic topology, Universidad Nacional Autónoma de México and UNESCO, Mexico City, 1958, pp. 129–144 (German). MR 0103280
F. Hirzebruch and D. Zagier, Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus, Invent. Math. 36 (1976), 57–113. MR 453649, DOI 10.1007/BF01390005
H. Hopf and H. Samelson, Ein Satz über die Wirkungsräume geschlossener Liescher Gruppen, Comment. Math. Helv. 13 (1941), 240–251 (German). MR 6546, DOI 10.1007/BF01378063
Dale Husemoller, Fibre bundles, 2nd ed., Graduate Texts in Mathematics, No. 20, Springer-Verlag, New York-Heidelberg, 1975. MR 0370578
Hervé Jacquet and Stephen Rallis, Symplectic periods, J. Reine Angew. Math. 423 (1992), 175–197. MR 1142486
Stephen S. Kudla and John J. Millson, Intersection numbers of cycles on locally symmetric spaces and Fourier coefficients of holomorphic modular forms in several complex variables, Inst. Hautes Études Sci. Publ. Math. 71 (1990), 121–172. MR 1079646
Serge Lang, Algebraic number theory, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London-Don Mills, Ont., 1970. MR 0282947
Ronnie Lee and Joachim Schwermer, Geometry and arithmetic cycles attached to $\textrm {SL}_3(\textbf {Z})$. I, Topology 25 (1986), no. 2, 159–174. MR 837619, DOI 10.1016/0040-9383(86)90037-6
John J. Millson, Cycles and harmonic forms on locally symmetric spaces, Canad. Math. Bull. 28 (1985), no. 1, 3–38. MR 778258, DOI 10.4153/CMB-1985-001-x

Geometric construction of homology for arithmetic groups

John J. Millson and M. S. Raghunathan, Geometric construction of cohomology for arithmetic groups. I, Geometry and analysis, Indian Acad. Sci., Bangalore, 1980, pp. 103–123. MR 592256
John W. Milnor and James D. Stasheff, Characteristic classes, Annals of Mathematics Studies, No. 76, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974. MR 0440554

Über den arithmetischen Begriff der Äquivalenz und über die endlichen Gruppen linearer ganzzahliger Substitutionen

100

David Mumford, Algebraic geometry. I, Grundlehren der Mathematischen Wissenschaften, No. 221, Springer-Verlag, Berlin-New York, 1976. Complex projective varieties. MR 0453732
Daniel Quillen, Elementary proofs of some results of cobordism theory using Steenrod operations, Advances in Math. 7 (1971), 29–56 (1971). MR 290382, DOI 10.1016/0001-8708(71)90041-7
J. Rohlfs, Arithmetisch definierte Gruppen mit Galoisoperation, Invent. Math. 48 (1978), no. 2, 185–205 (German). MR 507801, DOI 10.1007/BF01390250
J. Rohlfs, The Lefschetz number of an involution on the space of classes of positive definite quadratic forms, Comment. Math. Helv. 56 (1981), no. 2, 272–296. MR 630954, DOI 10.1007/BF02566213

Lefschetz numbers for automorphisms of finite order on arithmetic groups

Jürgen Rohlfs and Birgit Speh, Automorphic representations and Lefschetz numbers, Ann. Sci. École Norm. Sup. (4) 22 (1989), no. 3, 473–499. MR 1011990
J. Rohlfs and B. Speh, Lefschetz numbers and twisted stabilized orbital integrals, Math. Ann. 296 (1993), no. 2, 191–214. MR 1219899, DOI 10.1007/BF01445102
Jean-Pierre Serre, Cohomologie galoisienne, Lecture Notes in Mathematics, No. 5, Springer-Verlag, Berlin-New York, 1965 (French). With a contribution by Jean-Louis Verdier; Troisième édition, 1965. MR 0201444
Robert Steinberg, Endomorphisms of linear algebraic groups, Memoirs of the American Mathematical Society, No. 80, American Mathematical Society, Providence, R.I., 1968. MR 0230728
Jacques Tits, Tabellen zu den einfachen Lie Gruppen und ihren Darstellungen, Springer-Verlag, Berlin-New York, 1967 (German). MR 0218489