Torsion 0-cycles with modulus on affine varieties

Abstract

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 on it, the Chow group of zero cycles with modulus CH0(X vertical bar D) is torsion free, except possibly for p-torsion if the characteristic of k is p > 0. This generalizes to the relative setting classical results of Rojtman (for X smooth) and of Levine (for X singular). (C) 2017 Elsevier B.V. All rights reserved.