Chow group of 0-cycles with modulus and higher dimensional class field theory

TL;DR

This paper proves a special case of a conjecture on lisse l-adic sheaves over finite fields, linking higher dimensional class field theory with Chow groups of zero cycles with moduli, and introduces a refined Artin conductor in ramification theory.

Contribution

It establishes the rank one case of an existence conjecture connecting l-adic sheaves and higher dimensional class field theory, using Chow groups and a new refined Artin conductor.

Findings

Proved the rank one case of Deligne-Drinfeld conjecture.

Linked Chow groups with higher dimensional class field theory.

Constructed a cycle-theoretic refined Artin conductor.

Abstract

One of the main results of this paper is a proof of the rank one case of an existence conjecture on lisse l-adic sheaves on a smooth variety over a finite field due to Deligne and Drinfeld. The problem is translated into the language of higher dimensional class field theory over finite fields, which describes the abelian fundamental group by Chow groups of zero cycles with moduli. A key ingredient is the construction of a cycle theoretic avatar of refined Artin conductor in ramification theory originally studied by Kazuya Kato.