Zero Cycles on Singular surfaces

摘要

Let X be a reduced and projective singular surface over ? and let X→X be a resolution of singularities of X. We show that CH ~2(X)?CH~2(X) if and only if H~2(X, ΩiX|C)?H~2(X,ΩiX|C) for i = 0, 1. This verifies a conjecture of Srinivas. We also verify Bloch's conjecture for singular surfaces assuming it holds for smooth surfaces. As a byproduct, we give an application to projective modules on certain singular affine surfaces.