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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.

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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