%0 Journal Article %T K-regularity, cdh-fibrant Hochschild homology, and a conjecture of Vorst %A G. Corti£¿as %A C. Haesemeyer %A C. A. Weibel %J Mathematics %D 2006 %I arXiv %X In this paper we prove that for an affine scheme essentially of finite type over a field $F$ and of dimension $d$, $K_{d+1}$-regularity implies regularity, assuming that the characteristic of $F$ is zero. This verifies a conjecture of Vorst. %U http://arxiv.org/abs/math/0605367v1