Vanishing of negative -theory in positive characteristic

Abstract

AbstractWe show how a theorem of Gabber on alterations can be used to apply the work of Cisinski, Suslin, Voevodsky, and Weibel to prove that $K_n(X) \otimes \mathbb{Z}[{1}/{p}]= 0$ for$n < {-}\! \dim X$ where $X$ is a quasi-excellent noetherian scheme, $p$ is a prime that is nilpotent on $X$, and $K_n$ is the $K$-theory of Bass–Thomason–Trobaugh. This gives a partial answer to a question of Weibel.