Algebra & Number Theory
- Algebra Number Theory
- Volume 12, Number 6 (2018), 1431-1469.
Torsion in the 0-cycle group with modulus
We show, for a smooth projective variety over an algebraically closed field with an effective Cartier divisor , that the torsion subgroup can be described in terms of a relative étale cohomology for any prime . 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 -torsion) for when is reduced. We deduce applications to the problem of invariance of the prime-to- torsion in under an infinitesimal extension of .
Algebra Number Theory, Volume 12, Number 6 (2018), 1431-1469.
Received: 12 May 2017
Revised: 11 September 2017
Accepted: 15 February 2018
First available in Project Euclid: 25 October 2018
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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