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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. J. W. S. Cassels and A. Fröhlich (eds.), Algebraic number theory (Brighton, 1965), Academic Press, 1967. MR 35:6500
  • 3. C. Chevalley, La théorie du corps de classes, Ann. of Math. 41 (1940), 394-418. MR 2:38c
  • 4. H. Hasse, History of class field theory, In Cassels and Fröhlich [2], pp. 266-279. MR 36:1417
  • 5. D. Hilbert, The theory of algebraic number fields, Springer-Verlag, 1998. MR 99j:01027
  • 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. S. MacLane, Origins of the cohomology of groups, Enseign. Math. 24 (1978), 1-29. MR 81j:01030
  • 12. J. S. Milne, Arithmetic duality theorems, Academic Press, 1986. MR 88e:14028
  • 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. J. Neukirch, Class field theory, Springer-Verlag, 1986. MR 87i:11005
  • 16. -, Algebraic number theory, Springer-Verlag, 1999. Translated from the 1992 German edition by N. Schappacher. MR 2000m:11104
  • 17. J.-P. Serre, Local fields, Springer-Verlag, 1979. MR 82e:12016
  • 18. J.-P. Serre, Galois cohomology, Springer-Verlag, Berlin, 1997. Translated from the French by Patrick Ion and revised by the author. MR 98g:12007
  • 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. -, Basic number theory, Springer-Verlag, 1967. MR 38:3244

Review Information:

Reviewer: Fernando Q. Gouvêa
Affiliation: Colby College
Email: fqgouvea@colby.edu
Journal: Bull. Amer. Math. Soc. 39 (2002), 101-107
MSC (2000): Primary 11R34; Secondary 11-02, 11R23, 11S20, 11S25, 11S31, 12G05
Published electronically: October 10, 2001
Review copyright: © Copyright 2001 American Mathematical Society
American Mathematical Society