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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Fesenko reciprocity map

Authors: K. I. Ikeda and E. Serbest
Original publication: Algebra i Analiz, tom 20 (2008), nomer 3.
Journal: St. Petersburg Math. J. 20 (2009), 407-445
MSC (2000): Primary 11S20, 11S31
Published electronically: April 7, 2009
MathSciNet review: 2454454
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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.

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Additional Information

K. I. Ikeda
Affiliation: Department of Mathematics, Istanbul Bilgi University, Kurtuluş Deresi Cad. No. 47, Dolapdere, 34440 Beyoǧlu, Istanbul, Turkey
Address at time of publication: Department of Mathematics, Yeditepe University, 26 Aǧustos Yerleşimi, İnönü Mah., Kayışdaǧı Cad., 34755 Kadıköy, Istanbul, Turkey

E. Serbest
Affiliation: Department of Mathematics, Atilim University, Kizilcaşar Köyü, Incek, 06836 Gölbaşı, Ankara, Turkey

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 by editor(s): August 20, 2007
Published electronically: April 7, 2009
Dedicated: Dedicated to our teacher Mehpare Bilhan
Article copyright: © Copyright 2009 American Mathematical Society