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Fesenko reciprocity map
Author(s):
K.
I.
Ikeda;
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
Posted:
April 7, 2009
MathSciNet review:
2454454
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Additional information
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  , 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.
References:
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Additional Information:
K.
I.
Ikeda
Affiliation:
Department of Mathematics, Istanbul Bilgi University, Kurtulus Deresi Cad. No. 47, Dolapdere, 34440 Beyoglu, Istanbul, Turkey
Address at time of publication:
Department of Mathematics, Yeditepe University, 26 Agustos Yerlesimi, Inönü Mah., Kayisdagi Cad., 34755 Kadiköy, Istanbul, Turkey
Email:
ilhan@bilgi.edu.tr, ilhan.ikeda@yeditepe.edu.tr
E.
Serbest
Affiliation:
Department of Mathematics, Atilim University, Kizilcasar Köyü, Incek, 06836 Gölbasi, Ankara, Turkey
Email:
eserbest@atilim.edu.tr
DOI:
10.1090/S1061-0022-09-01054-1
PII:
S 1061-0022(09)01054-1
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):
20/AUG/2007
Posted:
April 7, 2009
Dedicated:
Dedicated to our teacher Mehpare Bilhan
Copyright of article:
Copyright
2009,
American Mathematical Society
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