Torsion in the 0-cycle group with modulus

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 {é}tale cohomology for any prime $l\ne p=\mathrm{char}(k)$. 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 $D$.

Final version, title changed, 32 pages, to appear in Algebra \& Number Theory journal