Torsion zero cycles with modulus on affine varieties

2016/04/21 by Federico Binda, Binda, Federico
Mathematics · #Algebraic Geometry and Number Theory #Advanced Differential Equations and Dynamical Systems #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1604.06294

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 D on it, the Kerz-Saito Chow group of zero cycles with modulus \rm 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 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.

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