Bass’ NK groups and cdh-fibrant Hochschild homology
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Bass’ NK groups and cdh-fibrant Hochschild homology

  • Author(s): Cortiñas, G.;
  • Haesemeyer, C.;
  • Walker, Mark E.;
  • Weibel, C.
  • et al.
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[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.

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