Vanishing of negative $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}K$-theory in positive characteristic. (17th July 2014)

• Record Type: Journal Article
• Authors: Kelly, Shane
• Is Part Of: Compositio mathematica. Volume 150:Number 8(2014)
• Page Start: 1425
• Page End: 1434
• Publication Date: 2014-07-17
• Subjects: 19D35, -- 14F20 (primary); negative K-groups, -- ldh-topology, -- alterations; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X14007301
• Languages: English
• ISSNs: 0010-437X

Abstract

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.