Bass' NK groups and cdh-fibrant Hochschild homology

G. Cortiñas, C. Haesemeyer, Mark E. Walker, C. Weibel

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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 Kn(R)=Kn(R[t]) implies Kn(R)=Kn(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.

Original languageEnglish (US)
Pages (from-to)421-448
Number of pages28
JournalInventiones Mathematicae
Issue number2
StatePublished - 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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