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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

Part of: Higher algebraic $K$-theory (Co)homology theory

Published online by Cambridge University Press:  17 July 2014

Shane Kelly
Shane Kelly*
Affiliation:
Interactive Research Center of Science, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo 152-8551, Japan email [email protected]
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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.

Keywords

negative K-groupsldh-topologyalterations

MSC classification

Secondary: 19D35: Negative $K$-theory, NK and Nil 14F20: Étale and other Grothendieck topologies and (co)homologies
Type
Research Article
Information
Compositio Mathematica , Volume 150 , Issue 8 , August 2014 , pp. 1425 - 1434
Copyright
© The Author 2014 

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