Torsion in the 0-cycle group with modulus

Krishna, Amalendu

doi:10.2140/ant.2018.12.1431

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Torsion in the 0-cycle group with modulus

Amalendu Krishna

Vol. 12 (2018), No. 6, 1431–1469

DOI: 10.2140/ant.2018.12.1431

Abstract

We show, for a smooth projective variety $X$ over an algebraically closed field $k$ with an effective Cartier divisor $D$ , that the torsion subgroup ${CH}_{0} (X | D) {l}$ can be described in terms of a relative étale cohomology for any prime $l \neq p = char (k)$ . This extends a classical result of Bloch, on the torsion in the ordinary Chow group, to the modulus setting. We prove the Roitman torsion theorem (including $p$ -torsion) for ${CH}_{0} (X | D)$ when $D$ is reduced. We deduce applications to the problem of invariance of the prime-to- $p$ torsion in ${CH}_{0} (X | D)$ under an infinitesimal extension of $D$ .

Keywords

Cycles with modulus, cycles on singular schemes, algebraic K-theory, étale cohomology

Mathematical Subject Classification 2010

Primary: 14C25

Secondary: 13F35, 14F30, 19F15

Milestones

Received: 12 May 2017

Revised: 11 September 2017

Accepted: 15 February 2018

Published: 6 October 2018

Authors

Amalendu Krishna
School of Mathematics Tata Institute of Fundamental Research Mumbai India

Vol. 12, No. 6, 2018