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Book Review

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Book Information:

Authors: Jürgen Neukirch, Alexander Schmidt and Kay Wingberg
Title: Cohomology of number fields
Additional book information: Grundlehren der mathematischen Wissenschaften, vol. 323, Springer-Verlag, 2000, 720 pp., ISBN 3-540-66671-0, $109.00

References [Enhancements On Off] (What's this?)

  • 1. Emil Artin and John Tate, Class field theory, 2nd ed., Advanced Book Classics, Addison-Wesley Publishing Company, Advanced Book Program, Redwood City, CA, 1990. MR 1043169
    E. Artin and J. Tate, Class field theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0223335
  • 2. Algebraic number theory, Proceedings of an instructional conference organized by the London Mathematical Society (a NATO Advanced Study Institute) with the support of the International Mathematical Union. Edited by J. W. S. Cassels and A. Fröhlich, Academic Press, London; Thompson Book Co., Inc., Washington, D.C., 1967. MR 0215665
  • 3. C. Chevalley, La théorie du corps de classes, Ann. of Math. 41 (1940), 394-418. MR 2:38c
  • 4. Helmut Hasse, History of class field theory, Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965), Thompson, Washington, D.C., 1967, pp. 266–279. MR 0218330
  • 5. David Hilbert, The theory of algebraic number fields, Springer-Verlag, Berlin, 1998. Translated from the German and with a preface by Iain T. Adamson; With an introduction by Franz Lemmermeyer and Norbert Schappacher. MR 1646901
  • 6. G. Hochschild, Local class field theory, Ann. of Math. 51 (1950), 331-347. MR 11:490a
  • 7. -, Note on Artin's reciprocity law, Ann. of Math. 52 (1950), 694-701. MR 12:315c
  • 8. G. Hochschild and T. Nakayama, Cohomology in class field theory, Ann. of Math. 55 (1952), 348-366. MR 13:916d
  • 9. H. Hopf, Fundamentalgruppe und zweite Bettische Gruppe, Comment. Math. Helv. 14 (1942), 257-309. MR 3:316e
  • 10. W. Hurewicz, Beiträge zur Topologie der Deformationen, Proc. Akad. Amsterdam 38 (1936), 112-119, 521-538, and 39 (1936), 117-125, 215-224.
  • 11. Saunders Mac Lane, Origins of the cohomology of groups, Enseign. Math. (2) 24 (1978), no. 1-2, 1–29. MR 497280
  • 12. J. S. Milne, Arithmetic duality theorems, Perspectives in Mathematics, vol. 1, Academic Press, Inc., Boston, MA, 1986. MR 881804
  • 13. T. Nakayama, Idèle-class factor sets and class field theory, Ann. of Math. 55 (1952), 73-84. MR 13:629a
  • 14. -, On a 3-cohomology class in class field theory and the relationship of algebra- and idèle-classes, Ann. of Math. 57 (1953), 1-14. MR 14:453a
  • 15. Jürgen Neukirch, Class field theory, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 280, Springer-Verlag, Berlin, 1986. MR 819231
  • 16. Jürgen Neukirch, Algebraic number theory, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 322, Springer-Verlag, Berlin, 1999. Translated from the 1992 German original and with a note by Norbert Schappacher; With a foreword by G. Harder. MR 1697859
  • 17. 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
  • 18. Jean-Pierre Serre, Galois cohomology, Springer-Verlag, Berlin, 1997. Translated from the French by Patrick Ion and revised by the author. MR 1466966
  • 19. S. Takahashi, Homology groups in class field theory, Tôhoku Math. J. 5 (1953), 8-11. MR 15:606b
  • 20. J. Tate, The higher dimensional cohomology groups of class field theory, Ann. of Math. 56 (1952), 294-297. MR 14:252b
  • 21. A. Weil, Sur la théorie du corps de classes, J. Math. Soc. Japan 3 (1951), 1-35. MR 13:439d
  • 22. André Weil, Basic number theory, Die Grundlehren der mathematischen Wissenschaften, Band 144, Springer-Verlag New York, Inc., New York, 1967. MR 0234930

Review Information:

Reviewer: Fernando Q. Gouvêa
Affiliation: Colby College
Email: fqgouvea@colby.edu
Journal: Bull. Amer. Math. Soc. 39 (2002), 101-107
Published electronically: October 10, 2001
Review copyright: © Copyright 2001 American Mathematical Society