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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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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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J. W. S. Cassels and A. Fröhlich (eds.), Algebraic number theory (Brighton, 1965), Academic Press, 1967. MR 0215665
C. Chevalley, La théorie du corps de classes, Ann. of Math. 41 (1940), 394-418. MR 2:38c
H. Hasse, History of class field theory, In Cassels and Fröhlich [2], pp. 266-279. MR 0218330
D. Hilbert, The theory of algebraic number fields, Springer-Verlag, 1998. 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
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W. Hurewicz, Beiträge zur Topologie der Deformationen, Proc. Akad. Amsterdam 38 (1936), 112-119, 521-538, and 39 (1936), 117-125, 215-224.
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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
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-, Algebraic number theory, Springer-Verlag, 1999. Translated from the 1992 German edition by N. Schappacher. MR 1697859
J.-P. Serre, Local fields, Springer-Verlag, 1979. MR 0554237
J.-P. 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
-, Basic number theory, Springer-Verlag, 1967. MR 0234930

Review Information:

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