Fesenko reciprocity map

Ikeda, K.; Serbest, E.

doi:10.1090/S1061-0022-09-01054-1

Fesenko reciprocity map
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by K. I. Ikeda and E. Serbest

St. Petersburg Math. J. 20 (2009), 407-445

DOI: https://doi.org/10.1090/S1061-0022-09-01054-1

Published electronically: April 7, 2009

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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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