One of the main results of this article is a proof of the rank-one case of an existence conjecture on lisse -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 of by Chow groups of -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.
"Chow group of -cycles with modulus and higher-dimensional class field theory." Duke Math. J. 165 (15) 2811 - 2897, 15 October 2016. https://doi.org/10.1215/00127094-3644902