Vanishing theorems for the negative K-theory of stacks
K-Theory and Homology
2019-12-18 v3 Algebraic Geometry
Algebraic Topology
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.
Keywords
Cite
@article{arxiv.1705.02295,
title = {Vanishing theorems for the negative K-theory of stacks},
author = {Marc Hoyois and Amalendu Krishna},
journal= {arXiv preprint arXiv:1705.02295},
year = {2019}
}
Comments
26 pages; v3: updated numbering to match published version; v2: final version, to appear in Annals of K-Theory