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 $K_{i} (X) [1 ∕ n] = 0$ if $n$ is nilpotent on $X$ and $K_{i} (X, ℤ ∕ n) = 0$ if $n$ 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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Keywords

algebraic $K\mkern-2mu$-theory, negative $K\mkern-2mu$-theory, algebraic stacks

Mathematical Subject Classification 2010

Primary: 19D35

Secondary: 14D23

Milestones

Received: 3 May 2018

Accepted: 29 January 2019

Published: 17 December 2019

Authors

Marc Hoyois
Department of Mathematics University of Southern California Los Angeles, CA United States

Amalendu Krishna
School of Mathematics Tata Institute of Fundamental Research Mumbai India

Vol. 4, No. 3, 2019

Marc Hoyois and Amalendu Krishna

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors