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Book Review
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Book Information
Author(s):
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(s):
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:
- 1.
- H. Cohn, Introduction to the construction of class fields, Cambridge Univ. Press, 1985. MR 812270
- 2.
- E. De Shalit, The explicit reciprocity law in local class field theory, Duke Math. J. 53 (1986), 163-176. MR 835803
- 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, Lecture Notes in Math., vol. 1016, Springer-Verlag, Berlin and New York, 1983, pp. 109-126. MR 726423
- 7.
- Kazuya Kato, Vanishing cycles, ramification of valuations, and class field theory, Duke Math. J. 55 (1987), 629-661. MR 904945
- 8.
- A. N. Parshin, Local class field theory, Proc. Steklov Inst. Math. 165 (1985), 157-185. 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
Additional Information:
Reviewer(s):
Michiel
Hazewinkel
Review Information:
Journal:
Bull. Amer. Math. Soc.
21
(1989),
95-101.
DOI:
10.1090/S0273-0979-1989-15772-8
PII:
S 0273-0979(1989)15772-8
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