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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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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?)

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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
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-, Note on Artin's reciprocity law, Ann. of Math. 52 (1950), 694-701. MR 12:315c
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-, Algebraic number theory, Springer-Verlag, 1999. Translated from the 1992 German edition by N. Schappacher. MR 1697859
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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
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-, 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