Zero-cycles and K-theory on normal surfaces

Abstract

In this paper we prove a formula, conjectured by Bloch and Srinivas [S2], which describes the Chow group of zero cycles of a normal quasi-projective surface X over a field, as an inverse limit of relative Chow groups of a desingularisation X̃ relative to multiples of the exceptional divisor. We then give several applications of this result -- a relative version of the famous Bloch Conjecture on 0-cycles, the triviality of the Chow group of 0-cycles for any 2-dimensional normal graded ̅Q-algebra (analogue of the Bloch-Beilinson Conjecture), and the analogue of the Roitman theorem for torsion 0-cycles in characteristic p > 0 for normal varieties (including the case of p-torsion).