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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?)

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  • 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
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  • 8. G. Hochschild and T. Nakayama, Cohomology in class field theory, Ann. of Math. 55 (1952), 348-366. MR 13:916d
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  • 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
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Review Information:

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