Vanishing of negative $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let ≤ =\leqslant \let \ge =\geqslant \let ≥ =\geqslant \def \Pr {Pr}\def \Fr {Fr}\def \Rey {Re}K$-theory in positive characteristic. (17th July 2014) - Kelly, Shane
Abstract: We 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.