Algebra & Number Theory

On the motivic class of an algebraic group

Federico Scavia

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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.

Article information

Algebra Number Theory, Volume 14, Number 4 (2020), 855-866.

Received: 7 August 2018
Revised: 16 July 2019
Accepted: 19 December 2019
First available in Project Euclid: 30 June 2020

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 14L15: Group schemes
Secondary: 14D23: Stacks and moduli problems

motivic class Grothendieck ring of stacks classifying stack algebraic torus


Scavia, Federico. On the motivic class of an algebraic group. Algebra Number Theory 14 (2020), no. 4, 855--866. doi:10.2140/ant.2020.14.855.

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