Zero-cycles and K-theory on normal surfaces

• 成果类型: Article
• 署名作者: Krishna, A; Srinivas, V
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/3597187
• 发表日期: 2002
• 页码: 155-195
• 关键词: singular-varieties; vector-bundles; bloch

摘要

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 (X) over tilde 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) over bar -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).