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.
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