Vol. 12, No. 6, 2018

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Torsion in the 0-cycle group with modulus

Amalendu Krishna

Vol. 12 (2018), No. 6, 1431–1469

We show, for a smooth projective variety X over an algebraically closed field k with an effective Cartier divisor D, that the torsion subgroup CH0(X|D){l} can be described in terms of a relative étale cohomology for any prime lp = 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 CH0(X|D) when D is reduced. We deduce applications to the problem of invariance of the prime-to-p torsion in CH0(X|D) under an infinitesimal extension of D.

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Cycles with modulus, cycles on singular schemes, algebraic K-theory, étale cohomology
Mathematical Subject Classification 2010
Primary: 14C25
Secondary: 13F35, 14F30, 19F15
Received: 12 May 2017
Revised: 11 September 2017
Accepted: 15 February 2018
Published: 6 October 2018
Amalendu Krishna
School of Mathematics
Tata Institute of Fundamental Research