Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
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?)

  • 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
  • J. W. S. Cassels and A. Fröhlich (eds.), Algebraic number theory, Academic Press, London; Thompson Book Co., Inc., Washington, D.C., 1967. MR 0215665
  • C. Chevalley, La théorie du corps de classes, Ann. of Math. 41 (1940), 394-418. MR 2:38c
  • 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
  • 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
  • G. Hochschild, Local class field theory, Ann. of Math. 51 (1950), 331-347. MR 11:490a -, Note on Artin's reciprocity law, Ann. of Math. 52 (1950), 694-701. MR 12:315c G. Hochschild and T. Nakayama, Cohomology in class field theory, Ann. of Math. 55 (1952), 348-366. MR 13:916d H. Hopf, Fundamentalgruppe und zweite Bettische Gruppe, Comment. Math. Helv. 14 (1942), 257-309. MR 3:316e W. Hurewicz, Beiträge zur Topologie der Deformationen, Proc. Akad. Amsterdam 38 (1936), 112-119, 521-538, and 39 (1936), 117-125, 215-224.
  • Saunders Mac Lane, Origins of the cohomology of groups, Enseign. Math. (2) 24 (1978), no. 1-2, 1–29. MR 497280
  • J. S. Milne, Arithmetic duality theorems, Perspectives in Mathematics, vol. 1, Academic Press, Inc., Boston, MA, 1986. MR 881804
  • T. Nakayama, Idèle-class factor sets and class field theory, Ann. of Math. 55 (1952), 73-84. MR 13:629a -, 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
  • Jürgen Neukirch, Class field theory, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 280, Springer-Verlag, Berlin, 1986. MR 819231
  • 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
  • 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
  • Jean-Pierre Serre, Galois cohomology, Springer-Verlag, Berlin, 1997. Translated from the French by Patrick Ion and revised by the author. MR 1466966
  • S. Takahashi, Homology groups in class field theory, Tôhoku Math. J. 5 (1953), 8-11. MR 15:606b J. Tate, The higher dimensional cohomology groups of class field theory, Ann. of Math. 56 (1952), 294-297. MR 14:252b A. Weil, Sur la théorie du corps de classes, J. Math. Soc. Japan 3 (1951), 1-35. MR 13:439d
  • 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