Bulletin of the American Mathematical Society

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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.

Harvey Cohn, Introduction to the construction of class fields, Cambridge Studies in Advanced Mathematics, vol. 6, Cambridge University Press, Cambridge, 1985. MR 812270

Ehud de Shalit, The explicit reciprocity law in local class field theory, Duke Math. J. 53 (1986), no. 1, 163–176. MR 835803, DOI 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.

Michiel Hazewinkel, Local class field theory is easy, Advances in Math. 18 (1975), no. 2, 148–181. MR 389858, DOI 10.1016/0001-8708(75)90156-5

5.

K. Iwasawa, Local class field theory, Iwanami-Shoten, 1980 (In Japanese).

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, DOI 10.1007/BFb0099960

Kazuya Kato, Vanishing cycles, ramification of valuations, and class field theory, Duke Math. J. 55 (1987), no. 3, 629–659. MR 904945, DOI 10.1215/S0012-7094-87-05532-3

A. N. Parshin, Local class field theory, Trudy Mat. Inst. Steklov. 165 (1984), 143–170 (Russian). Algebraic geometry and its applications. MR 752939

Jean-Pierre Serre, Sur les corps locaux à corps résiduel algébriquement clos, Bull. Soc. Math. France 89 (1961), 105–154 (French). MR 142534

A. Wiles, Higher explicit reciprocity laws, Ann. of Math. (2) 107 (1978), no. 2, 235–254. MR 480442, DOI 10.2307/1971143

1.

H. Cohn, Introduction to the construction of class fields, Cambridge Univ. Press, 1985. MR 0812270

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