Classification of Reductive Monoid Spaces Over an Arbitrary Field

In this semi-expository paper we review the notion of a spherical space. In particular we present some recent results of Wedhorn on the classification of spherical spaces over arbitrary fields. As an application, we introduce and classify reductive monoid spaces over an arbitrary field.Comment: This is the final versio

Torsion zero cycles with modulus on affine varieties

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.Comment: Final version. 12 pages, exposition improved. Several gaps in the proofs fixe