K. I. Ikeda, E. Serbest, “Fesenko Reciprocity Map”, Algebra i Analiz, 20:3 (2008), 112–162; St. Petersburg Math. J., 20:3 (2009), 407

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Algebra i Analiz, 2008, Volume 20, Issue 3, Pages 112–162 (Mi aa515)

This article is cited in 6 scientific papers (total in 6 papers)

Research Papers

Fesenko Reciprocity Map

K. I. Ikeda^a, E. Serbest^b

^a Department of Mathematics, Istanbul Bilgi University, Istanbul, Turkey
^b Department of Mathematics, Atilim University, Ankara, Turkey

Full-text PDF (564 kB) Citations (6)

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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

English version:
St. Petersburg Mathematical Journal, 2009, Volume 20, Issue 3, Pages 407–445
DOI: https://doi.org/10.1090/S1061-0022-09-01054-1

Bibliographic databases:

Document Type: Article

MSC: 11S20, 11S31

Language: English

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

Citation in format AMSBIB

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\by K.~I.~Ikeda, E.~Serbest

\paper Fesenko Reciprocity Map

\jour Algebra i Analiz

\yr 2008

\vol 20

\issue 3

\pages 112--162

\mathnet{http://mi.mathnet.ru/aa515}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2454454}

\zmath{https://zbmath.org/?q=an:1206.11138}

\transl

\jour St. Petersburg Math. J.

\yr 2009

\vol 20

\issue 3

\pages 407--445

\crossref{https://doi.org/10.1090/S1061-0022-09-01054-1}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000267497700005}

Linking options:

https://www.mathnet.ru/eng/aa515

https://www.mathnet.ru/eng/aa/v20/i3/p112

This publication is cited in the following 6 articles:

Fesenko I., “Class Field Theory, Its Three Main Generalisations, and Applications”, EMS Surv. Math. Sci., 8:1-2 (2021), 107–133
Fesenko I.B. Vostokov S.V. Yoon S.H., “Generalised Kawada-Satake Method For Mackey Functors in Class Field Theory”, Eur. J. Math., 4:3, 2, SI (2018), 953–987
Ikeda K.I., Serbest E., “Non-abelian local reciprocity law”, Manuscr. Math., 132:1-2 (2010), 19–49
Ikeda K.I., Serbest E., “Ramification theory in non-abelian local class field theory”, Acta Arith., 144:4 (2010), 373–393
Laubie F., Moioli O., “The Nottingham group and local class field theory”, J. Lond. Math. Soc. (2), 80:1 (2009), 191–211
St. Petersburg Math. J., 20:4 (2009), 593–624

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	444
Full-text PDF :	130
References:	66
First page:	5

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