### On a conjecture of Vorst

Let *k* be an infinite perfect field of positive characteristic
*p* and assume that strong resolution of singularities holds
over *k*. We prove that, as conjectured by Vorst,
a localization of a *d*-dimensional
commutative *k*-algebra *R* of finite type
is *K*_{d+1}-regular if and only if it is
regular.

Lars Hesselholt
<larsh@math.nagoya-u.ac.jp>