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$G$-theory of root stacks and equivariant $K\mkern-2mu$-theory

Ajneet Dhillon and Ivan Kobyzev
Vol. 4 (2019), No. 2, 151–183
DOI: 10.2140/akt.2019.4.151
Abstract

Using the description of the category of quasicoherent sheaves on a root stack, we compute the G-theory of root stacks via localization methods. We apply our results to the study of equivariant K-theory of algebraic varieties under certain conditions.

Keywords
root stack, quotient stack, equivariant $K\mkern-2mu$-theory, parabolic sheaves
Mathematical Subject Classification 2010
Primary: 14A20, 14L30, 19D10, 19E08
Milestones
Received: 31 May 2017
Revised: 22 November 2018
Accepted: 10 December 2018
Published: 16 June 2019
Authors
Ajneet Dhillon
Department of Mathematics
Middlesex College
University of Western Ontario
London, ON
Canada
Ivan Kobyzev
Department of Pure Mathematics
University of Waterloo
Waterloo, ON
Canada