\ell-adic class field theory for regular local rings

TL;DR

This paper establishes an dic version of class field theory for henselian regular local rings of equi-characteristic, assuming Galois symbol map surjectivity, extending Matsumi's prior work.

Contribution

It proves dic abelian class field theory for certain local rings, advancing the understanding of dic Galois representations in algebraic number theory.

Findings

Proves dic class field theory under specific conditions

Extends Matsumi's results to dic setting

Assumes surjectivity of Galois symbol maps

Abstract

In this paper, we prove the $\ell$-adic abelian class field theory for henselian regular local rings of equi-characteristic assuming the surjectivity of Galois symbol maps, which is a $\ell$-adic variant of a result of Matsumi [13].