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arXiv · 1705.02295

Vanishing theorems for the negative K-theory of stacks

Marc Hoyois·Amalendu Krishna
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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.

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Marc Hoyois, Amalendu Krishna. 2019-08-13. Vanishing theorems for the negative K-theory of stacks. https://doi.org/10.2140/akt.2019.4.439

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