Bass' NK groups and cdh-fibrant Hochschild homology

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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 Kähler 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.