Bass' NK groups and cd h-fibrant Hochschild homology

• 成果类型: Article
• 署名作者: Cortinas, G.; Haesemeyer, C.; Walker, Mark E.; Weibel, C.
• 署名单位: University of California System; University of California Los Angeles; University of Buenos Aires; University of Nebraska System; University of Nebraska Lincoln; Rutgers University System; Rutgers University New Brunswick
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-010-0253-z
• 发表日期: 2010
• 页码: 421-448
• 关键词: algebraic k-theory; cyclic homology; COHOMOLOGY; conjecture

摘要

The K-theory of a polynomial ring R[t] contains the K-theory of R as a summand. For R commutative and containing ae, we describe K (*)(R[t])/K (*)(R) in terms of Hochschild homology and the cohomology of Kahler differentials for the cdh topology. We use this to address Bass' question, whether K (n) (R)=K (n) (R[t]) implies K (n) (R)=K (n) (R[t (1),t (2)]). The answer to this question is affirmative when R is essentially of finite type over the complex numbers, but negative in general.