Vanishing theorems for the negative K-theory of stacks

Abstract

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.

26 pages; v3: updated numbering to match published version; v2: final version, to appear in Annals of K-Theory

References in corpus (1)

• Addendum: Étale dévissage, descent and pushouts of stacks

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• Algebraic K-theory of quasi-smooth blow-ups and cdh descent
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• $T$-equivariant motives of flag varieties