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On the mixed Tate property and the motivic class of the classifying stack of a finite group

Federico Scavia

Vol. 16 (2022), No. 10, 2265–2287
Abstract

Let G be a finite group, and let {BG} the class of its classifying stack BG in Ekedahl’s Grothendieck ring of algebraic -stacks K0(Stacks ). We show that if BG has the mixed Tate property, the invariants Hi({BG}) defined by Ekedahl are zero for all i0. We also extend Ekedahl’s construction of these invariants to fields of positive characteristic.

Keywords
mixed Tate, Grothendieck ring, classifying stack, algebraic group
Mathematical Subject Classification
Primary: 14A20, 14C15
Secondary: 14J10
Milestones
Received: 8 August 2020
Revised: 2 December 2021
Accepted: 1 February 2022
Published: 28 January 2023
Authors
Federico Scavia
Department of Mathematics
University of California
Los Angeles, CA
United States