On the motivic class of an algebraic group

Scavia, Federico

doi:10.2140/ant.2020.14.855

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On the motivic class of an algebraic group

Federico Scavia

Vol. 14 (2020), No. 4, 855–866

DOI: 10.2140/ant.2020.14.855

Abstract

Let $F$ be a field of characteristic zero admitting a biquadratic field extension. We give an example of a torus $G$ over $F$ whose classifying stack $B G$ is stably rational and such that ${B G} \neq {G}^{- 1}$ in the Grothendieck ring of algebraic stacks over $F$ . We also give an example of a finite étale group scheme $A$ over $F$ such that $B A$ is stably rational and ${B A} \neq 1$ .

Keywords

motivic class, Grothendieck ring of stacks, classifying stack, algebraic torus

Mathematical Subject Classification 2010

Primary: 14L15

Secondary: 14D23

Milestones

Received: 7 August 2018

Revised: 16 July 2019

Accepted: 19 December 2019

Published: 21 June 2020

Authors

Federico Scavia
University of British Columbia Vancouver BC Canada

Vol. 14, No. 4, 2020