Local abelian Kato-Parshin reciprocity law: A survey

Authors : Kazim İlhan IKEDA, Erol SERBEST

Pages : 1225-1250

Doi:10.15672/hujms.834042

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Publication Date : 2021-10-15

Article Type : Review Paper

Abstract :Let $K$ denote an $n$-dimensional local field. The aim of this expository paper is to survey the basic arithmetic theory of the $n$-dimensional local field $K$ together with its Milnor $K$-theory and Parshin topological $K$-theory; to review Kato`s ramification theory for finite abelian extensions of the $n$-dimensional local field $K$, and to state the local abelian higher-dimensional $K$-theoretic generalization of local abelian class field theory of Hasse, which is developed by Kato and Parshin. The paper is geared toward non-abelian generalization of this theory.
Keywords : higher dimensional local fields, Milnor K theory, local class field theory