Vanishing of negative $K$-theory in positive characteristic

Abstract

We show how a theorem of Gabber on alterations can be used to apply work of Cisinski, Suslin, Voevodsky, and Weibel to prove that $K_n(X)[1/p]=0$ 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.

9 pages. Final version. Accepted to Compositio Mathematica. The material (removed long ago) on presheaves with traces that appeared in the previous version can be found in the author's Ph.D. thesis

References in corpus (2)

• Descente par éclatements en K-théorie invariante par homotopie
• On the vanishing of negative K-groups

Cited by in corpus (3)

• Algebraic K-theory and descent for blow-ups
• A better comparison of cdh- and ldh-cohomologies
• The slice spectral sequence for singular schemes and applications