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|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).
Torsion 0-cycles with modulus on affine varieties / F. Binda. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 222:1(2018 Jan), pp. 61-74. [10.1016/j.jpaa.2017.03.004]
Torsion 0-cycles with modulus on affine varieties
F. Binda
2018
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|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).
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