Translator Disclaimer
2019 Vanishing theorems for the negative $K$-theory of stacks
Marc Hoyois, Amalendu Krishna
Ann. K-Theory 4(3): 439-472 (2019). DOI: 10.2140/akt.2019.4.439

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 if n is nilpotent on X and K i ( X , 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.

Citation

Download Citation

Marc Hoyois. Amalendu Krishna. "Vanishing theorems for the negative $K$-theory of stacks." Ann. K-Theory 4 (3) 439 - 472, 2019. https://doi.org/10.2140/akt.2019.4.439

Information

Received: 3 May 2018; Accepted: 29 January 2019; Published: 2019
First available in Project Euclid: 3 January 2020

zbMATH: 07146016
MathSciNet: MR4043465
Digital Object Identifier: 10.2140/akt.2019.4.439

Subjects:
Primary: 19D35
Secondary: 14D23

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

Rights: Copyright © 2019 Mathematical Sciences Publishers

JOURNAL ARTICLE
34 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.4 • No. 3 • 2019
MSP
Back to Top