Ikeda, K. I.Serbest, E.2024-07-052024-07-0520091061-00221547-737110.1090/S1061-0022-09-01054-12-s2.0-85009807696https://doi.org/10.1090/S1061-0022-09-01054-1https://hdl.handle.net/20.500.14411/1054Ikeda, Kazim Ilhan/0000-0001-6349-3541In 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 correspondenceArticleQ3Q4203407445WOS:0002674977000051