İkeda, Kazım İlhanSerbest, E.2021-01-182021-01-182009-061547-73711061-0022https://hdl.handle.net/11411/3130https://doi.org/10.1090/S1061-0022-09-01054-1In 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.eninfo:eu-repo/semantics/openAccessLocal fieldshigher-ramification theoryAPF extensionsFontaine-Wintenberger field of normsFesenko reciprocity mapnon-Abelian local class field theoryp-adic local Langlands correspondenceArticle2-s2.0-8500980769610.1090/S1061-0022-09-01054-1Q2WOS:000267497700005