1. Fesenko reciprocity map
- Author
-
Erol Serbest and Kâzim Ilhan Ikeda
- Subjects
Algebra ,Algebra and Number Theory ,Non-abelian class field theory ,Applied Mathematics ,Local class field theory ,Reciprocity (electromagnetism) ,Galois extension ,Mathematical proof ,Local field ,Analysis ,Mathematics - 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 works 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.
- Published
- 2009
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