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

Abstract

One of the main results of this article is a proof of the rank-one case of an existence conjecture on lisse ${\overline{\mathbb{Q}}}_{\ell }$-sheaves on a smooth variety $U$ 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 of $U$ by Chow groups of $0$-cycles with moduli. A key ingredient is the construction of a cycle-theoretic avatar of a refined Artin conductor in ramification theory originally studied by Kazuya Kato.