Bass' NK groups and cdh-fibrant Hochschild homology
Abstract
The K-theory of a polynomial ring R[t] contains the K-theory of R as a summand. For R commutative and containing , we describe K*(R[t])/K*(R) in terms of Hochschild homology and the cohomology of K\"ahler differentials for the cdh topology. We use this to address Bass' question, on whether Kn(R)=Kn(R[t]) implies Kn(R)=Kn(R[t1,t2]). The answer is positive over fields of infinite transcendence degree; the companion paper arXiv:1004.3829 provides a counterexample over a number field.
0