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Riemann-Hurwitz formula and p-adic Galois representations for number fields. (English) Zbl 0468.12004


MSC:

11R34 Galois cohomology
11R58 Arithmetic theory of algebraic function fields
14H52 Elliptic curves
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References:

[1] A. BRUMER, Galois groups of extensions of algebraic number fields with given ramifica-tion, Mich. Jour. Math. 13 (1966), 33-40. · Zbl 0141.04803 · doi:10.1307/mmj/1028999477
[2] C. CHEVALLEY AND A. WEIL, Uber das Verhalten der Integrale erster Gattung bei Auto morphismen des Funktionenkrpers, Hamb. Abh. 10 (1934), 358-361. Zentralblatt MATH: · Zbl 0009.16001 · doi:10.1007/BF02940687
[3] B. FERRERO AND L. WASHINGTON, The Iwasawa invariant p vanishes for abelian numbe fields, Ann. Math. 109 (1979), 377-395. JSTOR: · Zbl 0443.12001 · doi:10.2307/1971116
[4] K. Iwasawa, On -extensions of algebraic number fields, Bull. Amer. Math. Soc. 6 (1959), 183-226. · Zbl 0089.02402 · doi:10.1090/S0002-9904-1959-10317-7
[5] K. Iwasawa, On Zrextensions of algebraic number fields, Ann. Math. 98 (1973), 246-326 JSTOR: · Zbl 0285.12008 · doi:10.2307/1970784
[6] Y. KIDA, ^-extensions of CM-fields and cyclotomic invariants, J. Number Theory 1 (1980), 519-528. · Zbl 0455.12007 · doi:10.1016/0022-314X(80)90042-6
[7] S. LANG, Rapport sur la Cohomologie des Groupes, W. A. Benjamin, Inc., New York Amsterdam, 1966. · Zbl 0171.28903
[8] J. -P. SERRE, Corps Locaux, Hermann, Paris, 1962
[9] J. -P. SERRE, Cohomologie Galoisienne, Lecture Notes in Math. 5, Springer-Verlag, Berlin Heidelberg-New York, 1964.
[10] K. WINGBERG, Die Einheitengruppe von p-Erweiterungen regular p-adischer Zahlkrpe als Galoismodul, Jour, fur die reine u. angew. Math. 305 (1979), 206-214. · Zbl 0393.12024 · doi:10.1515/crll.1979.305.206
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