Bass’ NK groups and cd h-fibrant Hochschild homology

Authors

• G. Cortiñas, Ciudad Universitaria Pab 1Follow
• C. Haesemeyer, University of California, Los AngelesFollow
• Mark E. Walker, University of Nebraska-LincolnFollow
• C. Weibel, Rutgers UniversityFollow

Document Type

Article

Date of this Version

2010

Citation

Invent math (2010) 181: 421–448

Comments

© The Author(s) 2010.

Abstract

The K-theory of a polynomial ring R[t ] contains the K-theory of R as a summand. For R commutative and containing Q, we describe K∗(R[t ])/K∗(R) in terms of Hochschild homology and the cohomology of Kähler 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[t₁, t₂]). The answer to this question is affirmative when R is essentially of finite type over the complex numbers, but negative in general.