栈的负k理论的消失定理

IF 0.5 Q3 MATHEMATICS Annals of K-Theory Pub Date : 2017-05-05 DOI:10.2140/akt.2019.4.439

Marc Hoyois, A. Krishna

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引用次数: 18

摘要

证明了拟dm叠的同伦代数k理论满足cdh-下降。我们利用这一下降结果证明了如果X是Noetherian驯服拟dm堆栈且i < -dim(X)，则K_i(X)[1/n] = 0 (resp。K_i(X, Z/n) = 0)，条件是n在X上幂零。在X上是可逆的)。我们的下降和消失的结果更普遍地适用于某些Artin堆栈，这些堆栈的稳定器是有限群格式由乘型群格式的扩展。

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Vanishing theorems for the negative K-theory of stacks

We prove that the homotopy algebraic K-theory of tame quasi-DM stacks satisfies cdh-descent. We apply this descent result to prove that if X is a Noetherian tame quasi-DM stack and i < -dim(X), then K_i(X)[1/n] = 0 (resp. K_i(X, Z/n) = 0) provided that n is nilpotent on X (resp. is invertible on X). Our descent and vanishing results apply more generally to certain Artin stacks whose stabilizers are extensions of finite group schemes by group schemes of multiplicative type.

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