Algebra & Number Theory

Torsion in the 0-cycle group with modulus

Amalendu Krishna

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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

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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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14C25: Algebraic cycles
Secondary: 13F35: Witt vectors and related rings 14F30: $p$-adic cohomology, crystalline cohomology 19F15: Symbols and arithmetic [See also 11R37]

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


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.

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