An Artin-Rees theorem in Κ-theory and applications to zero cycles

Abstract

For the smooth normalization f : ̅X → X of a singular variety X over a field k of characteristic zero, we show that for any conducting subscheme Y for the normalization, and for any i ε Z, the natural map K_i(X, ̅X, nY) → K_i(X, ̅X, Y) is zero for all sufficiently large n. As an application, we prove a formula for the Chow group of zero cycles on a quasi-projective variety X over k with Cohen-Macaulay isolated singularities, in terms of an inverse limit of the relative Chow groups of a desingularization ˜X relative to the multiples of the exceptional divisor. We use this formula to verify a conjecture of Srinivas about the Chow group of zero cycles on the affine cone over a smooth projective variety which is arithmetically Cohen-Macaulay.