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Bulletin of the American Mathematical Society

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

Book Review

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Book Information:

Author: Jürgen Neukirch
Title: Class field theory
Additional book information: Grundlehren der Mathematischen Wissenschaften, vol. 280, Springer-Verlag, Berlin, Heidelberg, New York, and Tokyo, 1986, $29.50. ISBN 0-387-15251-2.

Author: Kenkichi Iwasawa
Title: Local class field theory
Additional book information: Oxford Mathematical Monographs, Oxford University Press, New York and Clarendon Press, Oxford, 1986, viii + 155 pp., $39.95. ISBN 0-19-504030-9.

References [Enhancements On Off] (What's this?)

  • 1. Harvey Cohn, Introduction to the construction of class fields, Cambridge Studies in Advanced Mathematics, vol. 6, Cambridge University Press, Cambridge, 1985. MR 812270
  • 2. Ehud de Shalit, The explicit reciprocity law in local class field theory, Duke Math. J. 53 (1986), no. 1, 163–176. MR 835803, https://doi.org/10.1215/S0012-7094-86-05311-1
  • 3. M. Hazewinkel, Classes de corps local, Appendice dans M. Demazure, P. Gabriel, Groupes algébriques, tome 1, North-Holland, 1971.
  • 4. M. Hazewinkel, Local class field theory is easy, Adv. in Math. 18 (1975), 148-181. MR 389858
  • 5. K. Iwasawa, Local class field theory, Iwanami-Shoten, 1980 (In Japanese).
  • 6. Kazuya Kato, Class field theory and algebraic 𝐾-theory, Algebraic geometry (Tokyo/Kyoto, 1982) Lecture Notes in Math., vol. 1016, Springer, Berlin, 1983, pp. 109–126. MR 726423, https://doi.org/10.1007/BFb0099960
  • 7. Kazuya Kato, Vanishing cycles, ramification of valuations, and class field theory, Duke Math. J. 55 (1987), no. 3, 629–659. MR 904945, https://doi.org/10.1215/S0012-7094-87-05532-3
  • 8. A. N. Parshin, Local class field theory, Trudy Mat. Inst. Steklov. 165 (1984), 143–170 (Russian). Algebraic geometry and its applications. MR 752939
  • 9. J.-P. Serre, Sur les corps locaux à corps résiduely algébriquement clos, Bull. Soc. Math. France 89 (1961), 105-154. MR 142534
  • 10. A. Wiles, Higher explicit reciprocity laws, Ann. of Math (2) 107 (1987), 235-254. MR 480442

Review Information:

Reviewer: Michiel Hazewinkel
Journal: Bull. Amer. Math. Soc. 21 (1989), 95-101
DOI: https://doi.org/10.1090/S0273-0979-1989-15772-8
American Mathematical Society