Vol. 14, No. 4, 2020

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On the motivic class of an algebraic group

Federico Scavia

Vol. 14 (2020), No. 4, 855–866

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 BG is stably rational and such that {BG}{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 BA is stably rational and {BA}1.

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motivic class, Grothendieck ring of stacks, classifying stack, algebraic torus
Mathematical Subject Classification 2010
Primary: 14L15
Secondary: 14D23
Received: 7 August 2018
Revised: 16 July 2019
Accepted: 19 December 2019
Published: 21 June 2020
Federico Scavia
University of British Columbia
Vancouver BC