Cyclic homology, cdh-cohomology and negative K-theory

• 成果类型: Article
• 署名作者: Cortinas, G.; Haesemeyer, C.; Schlichting, M.; Weibel, C.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2008.167.549
• 发表日期: 2008
• 页码: 549-573
• 关键词: simplicial presheaves; descent; CATEGORIES; excision; MODEL

摘要

We prove a blow-up formula for cyclic homology which we use to show that infinitesimal K-theory satisfies cdh-descent. Combining that result with some computations of the cdh-cohomology of the sheaf of regular functions, we verify a conjecture of Weibel predicting the vanishing of algebraic K-theory of a scheme in degrees less than minus the dimension of the scheme, for schemes essentially of finite type over a field of characteristic zero.