K-regularity, cdh-fibrant Hochschild homology, and a conjecture of Vorst
  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. 
G. Corti\~nas, C. Haesemeyer, C. A. Weibel