Annals of K-Theory

Algebraic $K$-theory of quotient stacks

Amalendu Krishna and Charanya Ravi

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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