  In this note we show that given a smooth affine variety $X$ over an
algebraically closed field $k$ and an effective (possibly non reduced) Cartier
divisor $D$ on it, the Kerz-Saito Chow group of zero cycles with modulus ${\rm
CH}_0(X|D)$ is torsion free, except possibly for $p$-torsion if the
characteristic of $k$ is $p>0$. This generalizes to the relative setting
classical theorems of Rojtman (for $X$ smooth) and of Levine (for $X$
singular). A stronger version of this result, that encompasses $p$-torsion as
well, was proven with a different and more sophisticated method by A. Krishna
and the author in another paper.
