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

Ivan B. Fesenko, Sergei V. Vostokov, Seok Ho Yoon

Research output: Contribution to journalArticlepeer-review

Abstract

We propose and study a generalised Kawada–Satake method for Mackey functors in the class field theory of positive characteristic. The root of this method is in the use of explicit pairings, such as the Artin–Schreier–Witt pairing, for groups describing abelian extensions. We separate and simplify the algebraic component of the method and discuss a relation between the existence theorem in class field theory and topological reflexivity with respect to the explicit pairing. We apply this method to derive higher local class field theory of positive characteristic, using advanced properties of topological Milnor K-groups of such fields.

Original languageEnglish
Pages (from-to)953-987
Number of pages35
JournalEuropean Journal of Mathematics
Volume4
Issue number3
DOIs
StatePublished - 1 Sep 2018

Scopus subject areas

  • Mathematics(all)

Keywords

  • Class field theory
  • Higher class field theory
  • Higher fields
  • Reflexivity for non-locally compact groups
  • Witt vectors

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