## Algebra & Number Theory

### Torsion in the 0-cycle group with modulus

Amalendu Krishna

#### 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 $l ≠ p = char ( k )$. 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 $D$.

#### Article information

Source
Algebra Number Theory, Volume 12, Number 6 (2018), 1431-1469.

Dates
Revised: 11 September 2017
Accepted: 15 February 2018
First available in Project Euclid: 25 October 2018

https://projecteuclid.org/euclid.ant/1540432834

Digital Object Identifier
doi:10.2140/ant.2018.12.1431

Mathematical Reviews number (MathSciNet)
MR3864203

Zentralblatt MATH identifier
06973916

#### Citation

Krishna, Amalendu. Torsion in the 0-cycle group with modulus. Algebra Number Theory 12 (2018), no. 6, 1431--1469. doi:10.2140/ant.2018.12.1431. https://projecteuclid.org/euclid.ant/1540432834

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