Duke Mathematical Journal

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

Moritz Kerz and Shuji Saito

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Abstract

One of the main results of this article is a proof of the rank-one case of an existence conjecture on lisse Q¯-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
Received: 6 May 2014
Revised: 24 October 2015
First available in Project Euclid: 31 August 2016

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1472655264

Digital Object Identifier
doi:10.1215/00127094-3644902

Mathematical Reviews number (MathSciNet)
MR3557274

Zentralblatt MATH identifier
06656236

Subjects
Primary: 14H30: Coverings, fundamental group [See also 14E20, 14F35]
Secondary: 14E22: Ramification problems [See also 11S15]

Keywords
Smooth I-adic Chow group modulus higher-dimensional class field theory ramification theory refined Artin theory

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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