Journal article
Bass' NK groups and cdh-fibrant Hochschild homology
G Cortiñas, C Haesemeyer, ME Walker, C Weibel
Inventiones Mathematicae | Published : 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 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. © 2010 The Author(s).
Grants
Awarded by National Science Foundation
Funding Acknowledgements
[ "Cortinas' research was partially supported by Conicet and partially supported by grants PICT 2006-00836, UBACyT X051, PIP 112-200801-00900, and MTM2007-64704.", "Haesemeyer's research was partially supported by NSF grant DMS-0652860.", "Walker's research was partially supported by NSF grant DMS-0601666.", "Weibel's research was supported by NSA grant MSPF-04G-184 and the Oswald Veblen Fund." ]