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Book Information:
Authors:
Skip Garibaldi,
Alexander Merkurjev and
Jean-Pierre Serre
Title:
Cohomological invariants in Galois cohomology
Additional book information:
University Lecture Series, vol. 28, American Mathematical Society,
Providence, RI,
2003,
vii+168 pp.,
ISBN 0-8218-3287-5,
$35.00$
Jón Kr. Arason, Cohomologische invarianten quadratischer Formen, J. Algebra 36 (1975), no. 3, 448–491 (French). MR 389761, DOI 10.1016/0021-8693(75)90145-3
Nicolas Bourbaki, Éléments d’histoire des mathématiques, Hermann, Paris, 1969 (French). Deuxième édition revue, corrigée, augmentée. MR 0243970
Richard Elman and T. Y. Lam, Classification theorems for quadratic forms over fields, Comment. Math. Helv. 49 (1974), 373–381. MR 351997, DOI 10.1007/BF02566738
Carl Friedrich Gauss, Disquisitiones arithmeticae, Springer-Verlag, New York, 1986. Translated and with a preface by Arthur A. Clarke; Revised by William C. Waterhouse, Cornelius Greither and A. W. Grootendorst and with a preface by Waterhouse. MR 837656
5. F. Q. Gouvêa (Reviewer). Cohomology of number fields by Jürgen Neukirch, Alexander Schmidt, and Kay Wingberg. Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 1, 101-107.
Max-Albert Knus, Alexander Merkurjev, Markus Rost, and Jean-Pierre Tignol, The book of involutions, American Mathematical Society Colloquium Publications, vol. 44, American Mathematical Society, Providence, RI, 1998. With a preface in French by J. Tits. MR 1632779, DOI 10.1090/coll/044
Saunders Mac Lane, Origins of the cohomology of groups, Enseign. Math. (2) 24 (1978), no. 1-2, 1–29. MR 497280
A. S. Merkur′ev and A. A. Suslin, $K$-cohomology of Severi-Brauer varieties and the norm residue homomorphism, Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), no. 5, 1011–1046, 1135–1136 (Russian). MR 675529
J. Mináč and Z. Reichstein, Trace forms of Galois extensions in the presence of a fourth root of unity, Int. Math. Res. Not. 8 (2004), 389–410. MR 2036337, DOI 10.1155/S1073792804130456
Jean-Pierre Serre, Cohomologie galoisienne: progrès et problèmes, Astérisque 227 (1995), Exp. No. 783, 4, 229–257 (French, with French summary). Séminaire Bourbaki, Vol. 1993/94. MR 1321649
J.-P. Serre, A course in arithmetic, Graduate Texts in Mathematics, No. 7, Springer-Verlag, New York-Heidelberg, 1973. Translated from the French. MR 0344216
Jean-Pierre Serre, Cohomologie galoisienne, 5th ed., Lecture Notes in Mathematics, vol. 5, Springer-Verlag, Berlin, 1994 (French). MR 1324577, DOI 10.1007/BFb0108758
Jean-Pierre Serre, Local fields, Graduate Texts in Mathematics, vol. 67, Springer-Verlag, New York-Berlin, 1979. Translated from the French by Marvin Jay Greenberg. MR 554237
Hermann Weyl, The classical groups, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997. Their invariants and representations; Fifteenth printing; Princeton Paperbacks. MR 1488158
- 1.
- J. K. Arason. Cohomologische invarianten quadratischer Formen. J. Algebra 36 (1975), no. 3, 448-491. MR 0389761
- 2.
- N. Bourbaki. Éléments d'histoire des mathématiques, deuxième édition revue, corrigée, augmentée. Paris: Hermann, 1969. MR 0243970
- 3.
- R. Elman and T. Y. Lam. Classification theorems for quadratic forms over fields. Comment. Math. Helv. 49 (1974), 373-381. MR 0351997
- 4.
- C. F. Gauss. Disquisitiones arithmeticae. Sectio quarta de congruentiis secundi gradus, art. 268. Werke, vol. 1, 301-304. Hildesheim: Georg Olms Verlag, 1973. MR 0837656
- 5.
- F. Q. Gouvêa (Reviewer). Cohomology of number fields by Jürgen Neukirch, Alexander Schmidt, and Kay Wingberg. Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 1, 101-107.
- 6.
- M.-A. Knus, A. Merkurjev, M. Rost, and J.-P. Tignol. The book of involutions. Colloquium Publications, vol. 44. Providence, RI: American Mathematical Society, 1998. MR 1632779
- 7.
- S. Mac Lane. Origins of the cohomology of groups. Enseign. Math. (2) 24 (1978), no. 1-2, 1-29. MR 0497280
- 8.
- A. S. Merkurjev and A. A. Suslin.
-cohomology of Severi-Brauer varieties and the norm residue homomorphism (Russian). Izv. Akad. Nauk SSSR 46 (1982), 1011-1046. English translation, Math. USSR Izv. 21 (1983), 307-340. MR 0675529
- 9.
- J. Minác and Z. Reichstein. Trace forms of Galois extensions in the presence of a fourth root of unity. Int. Math. Res. Not. 2004, no. 8, 389-410. MR 2036337
- 10.
- J-P. Serre. Cohomologie galoisienne: progrès et problèmes. Séminaire Bourbaki, 46ème année, 1993-1994, n
783. Astérisque 227 (1995): 229-257. MR 1321649
- 11.
- J-P. Serre. A course in arithmetic. Translation (1973) of Cours d'arithmétique. New York: Springer-Verlag, 1973. MR 0344216
- 12.
- J-P. Serre. Galois cohomology. Translation (1997), subsequently corrected, of the fifth, revised edition (1994) of Cohomologie galoisienne. Berlin: Springer-Verlag, 2002. MR 1324577
- 13.
- J-P. Serre. Local fields. Translation (1979) of the second edition (1968) of Corps locaux. Graduate texts in mathematics, vol. 67. New York: Springer-Verlag, 1979. MR 0554237
- 14.
- H. Weyl. The classical groups: their invariants and representations, 2nd ed. Princeton: Princeton University Press, 1946. MR 1488158
Review Information:
Reviewer:
John Swallow
Affiliation:
Davidson College
Email:
joswallow@davidson.edu
Journal:
Bull. Amer. Math. Soc.
42 (2005), 93-98
Published electronically:
September 24, 2004
Review copyright:
© Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
