Iwasawa, Kenkichi Riemann-Hurwitz formula and p-adic Galois representations for number fields. (English) Zbl 0468.12004 Tohoku Math. J., II. Ser. 33, 263-288 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 8 ReviewsCited in 41 Documents MSC: 11R34 Galois cohomology 11R58 Arithmetic theory of algebraic function fields 14H52 Elliptic curves Keywords:Riemann-Hurwitz formula; Galois cohomology; Iwasawa my invariant; genus of compact Riemann surfaces Citations:Zbl 0455.12007; Zbl 0009.16001 PDFBibTeX XMLCite \textit{K. Iwasawa}, Tôhoku Math. J. (2) 33, 263--288 (1981; Zbl 0468.12004) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.