Vol. 3, No. 2, 2018

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Algebraic $K\mskip-2mu$-theory of quotient stacks

Amalendu Krishna and Charanya Ravi

Vol. 3 (2018), No. 2, 207–233

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.

algebraic $K\mskip-2mu$-theory, singular schemes, groups actions, stacks
Mathematical Subject Classification 2010
Primary: 19E08
Secondary: 14L30
Received: 12 October 2016
Revised: 17 July 2017
Accepted: 1 August 2017
Published: 24 March 2018
Amalendu Krishna
School of Mathematics
Tata Institute of Fundamental Research
Charanya Ravi
Department of Mathematics
University of Oslo