Generalized Fesenko reciprocity map

Abstract

Abstract. The paper is a natural continuation and generalization of the works of Fesenko and of the authors. Fesenko's theory is carried over to infinite APF Galois extensions L over a local field K with a finite residue-class field is constructed, and its functorial and ramification-theoretic properties are studied. The case of d = 1 recovers the theory of Fesenko.

Class field theory, its three main generalisations, and applications

“…Koch-de Shalit's metabelian local class field theory, which is of SCFT type, may be viewed as one of the developments related to this theorem. A related development is general arithmetic non-abelian CFT, which is of GCFT type, it includes local theory for arithmetically profinite extensions, with its existence theorem and compatibility with ramification theory (Fesenko [7], Ikeda-Serbest [23][24][25][26]), and some global theory (Ikeda [22]).…”

Generalised Kawada–Satake method for Mackey functors in class field theory

“…Finding new examples of fields for which there is a kind of class field theory but the existing class field mechanism axioms are too restrictive to be applicable seems to be a never ending process. More recent examples include higher class field theory [4], p-class field theory [5], [6], general class field theory [7] (where, unusually, there is no induction of the degree of extension), non-commutative local class field theories [8], [9], [16], [17], [18].…”