1 results
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
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- Journal:
- Compositio Mathematica / Volume 150 / Issue 8 / August 2014
- Published online by Cambridge University Press:
- 17 July 2014, pp. 1425-1434
- Print publication:
- August 2014
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- Article
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- You have access
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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.
