Zero cycles on a threefold with isolated singularities

Abstract

We prove a formula for the Chow group of zero cycles on a quasiprojective threefold X over a field of characteristic zero with Cohen-Macaulay isolated singularities, in terms of an inverse limit of relative Chow groups of a desingularization X˜ relative to multiples of the exceptional divisor. As an application, we give a necessary and sufficient condition for the Chow group of 0-cycles on the affine cone over a smooth projective and arithmetically Cohen-Macaulay surface to vanish. This partially answers a conjecture of Srinivas in affirmative.