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This article is cited in 6 scientific papers (total in 6 papers)
Research Papers
Fesenko Reciprocity Map
K. I. Ikedaa, E. Serbestb a Department of Mathematics, Istanbul Bilgi University, Istanbul, Turkey
b Department of Mathematics, Atilim University, Ankara, Turkey
Abstract:
In recent papers Fesenko has defined the non-Abelian local reciprocity map for every totally ramified arithmetically profinite ($APF$) Galois extension of a given local field $K$, by extending the work of
Hazewinkel and Neukirch–Iwasawa. The theory of Fesenko extends the previous non-Abelian generalizations
of local class field theory given by Koch –de Shalit and by A. Gurevich. In this paper, which is
research-expository in nature, we give a detailed account of Fesenko's work, including all the skipped proofs.
Keywords:
local fields, higher-ramification theory, $APF$-extensions Fontaine–Wintenberger field of norms, Fesenko reciprocity map, non-Abelian local class field theory, $p$-adic local Langlands correspondence.
Received: 20.08.2007
Citation:
K. I. Ikeda, E. Serbest, “Fesenko Reciprocity Map”, Algebra i Analiz, 20:3 (2008), 112–162; St. Petersburg Math. J., 20:3 (2009), 407–445
Linking options:
https://www.mathnet.ru/eng/aa515 https://www.mathnet.ru/eng/aa/v20/i3/p112
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