Bass’ NK groups and cdh-fibrant Hochschild homology
- Author(s): Cortiñas, G.
- Haesemeyer, C.
- Walker, Mark E.
- Weibel, C.
- et al.
Published Web Locationhttps://doi.org/10.1007/s00222-010-0253-z
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[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.