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Class group rank relations in \(Z_p\)-extensions. (English) Zbl 0516.12012

MSC:
11R58 Arithmetic theory of algebraic function fields
11R18 Cyclotomic extensions
11R23 Iwasawa theory
11R37 Class field theory
14H30 Coverings of curves, fundamental group
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References:
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[2] H. Hasse: Vorlesungen über Klassenkörpertheorie, Physica-Verlag. Wurzburg, 1967 · Zbl 0148.28005
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[5] Y. Kida: Cyclotomic ?p -extensions of J-fields, Journal of Number Theory 14, 340-352 (1982) · Zbl 0493.12015 · doi:10.1016/0022-314X(82)90069-5
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[7] M. L. Madan and Sat Pal: Galois cohomology and a theorem of E. Artin, Number Theory and Algebra, © 1977 Academic Press, Inc.
[8] M. Moriya; Über die Struktur der Divisorenklassen einer zyklischen Erweiterung von Primzahlgrad über einem algebraischen Funktionenkörper, Tôhoku Math. J. 48 (1941), 43-54 · JFM 67.0105.03
[9] I. R- ?afarevi?: On p-extensions, Amer. Math. Soc. Trans. Series II, vol. 4, 59-71 (1954)
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[11] E. Weiss: Cohomology of Groups, Academic Press (1969) · Zbl 0192.34204
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