Duke Mathematical Journal
- Duke Math. J.
- Volume 165, Number 15 (2016), 2811-2897.
Chow group of -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 -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.
Duke Math. J. Volume 165, Number 15 (2016), 2811-2897.
Received: 6 May 2014
Revised: 24 October 2015
First available in Project Euclid: 31 August 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14H30: Coverings, fundamental group [See also 14E20, 14F35]
Secondary: 14E22: Ramification problems [See also 11S15]
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