Annals of K-Theory

Algebraic $K$-theory of quotient stacks

Amalendu Krishna and Charanya Ravi

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Abstract

We prove some fundamental results like localization, excision, Nisnevich descent, and the regular blow-up formula for the algebraic K -theory of certain stack quotients of schemes with affine group scheme actions. We show that the homotopy K -theory of such stacks is homotopy invariant. This implies a similar homotopy invariance property of the algebraic K -theory with coefficients.

Article information

Source
Ann. K-Theory, Volume 3, Number 2 (2018), 207-233.

Dates
Received: 12 October 2016
Revised: 17 July 2017
Accepted: 1 August 2017
First available in Project Euclid: 4 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.akt/1522807258

Digital Object Identifier
doi:10.2140/akt.2018.3.207

Mathematical Reviews number (MathSciNet)
MR3781427

Zentralblatt MATH identifier
06861673

Subjects
Primary: 19E08: $K$-theory of schemes [See also 14C35]
Secondary: 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]

Keywords
algebraic $K\mskip-2mu$-theory singular schemes groups actions stacks

Citation

Krishna, Amalendu; Ravi, Charanya. Algebraic $K$-theory of quotient stacks. Ann. K-Theory 3 (2018), no. 2, 207--233. doi:10.2140/akt.2018.3.207. https://projecteuclid.org/euclid.akt/1522807258


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