## Duke Mathematical Journal

### 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.

#### Article information

Source
Duke Math. J., Volume 165, Number 15 (2016), 2811-2897.

Dates
Revised: 24 October 2015
First available in Project Euclid: 31 August 2016

https://projecteuclid.org/euclid.dmj/1472655264

Digital Object Identifier
doi:10.1215/00127094-3644902

Mathematical Reviews number (MathSciNet)
MR3557274

Zentralblatt MATH identifier
06656236

Subjects

#### Citation

Kerz, Moritz; Saito, Shuji. Chow group of $0$ -cycles with modulus and higher-dimensional class field theory. Duke Math. J. 165 (2016), no. 15, 2811--2897. doi:10.1215/00127094-3644902. https://projecteuclid.org/euclid.dmj/1472655264

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