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Abstract
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We prove that the homotopy algebraic
-theory of
tame quasi-DM stacks satisfies cdh-descent. We apply this descent result to prove that if
is a Noetherian tame
quasi-DM stack and
,
then
if
is nilpotent
on
and
if
is invertible
on
.
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
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Mathematical Subject Classification 2010
Primary: 19D35
Secondary: 14D23
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Milestones
Received: 3 May 2018
Accepted: 29 January 2019
Published: 17 December 2019
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