CHOW GROUP OF 0-CYCLES WITH MODULUS AND HIGHER-DIMENSIONAL CLASS FIELD THEORY

One of the main results of this article is a proof of the rank-one case of an existence conjecture on lisse (Q) over bar (l)-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.