Algebra & Number Theory

On the motivic class of an algebraic group

Federico Scavia

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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 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

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

Dates
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
https://projecteuclid.org/euclid.ant/1593482420

Digital Object Identifier
doi:10.2140/ant.2020.14.855

Mathematical Reviews number (MathSciNet)
MR4114058

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

Keywords
motivic class Grothendieck ring of stacks classifying stack algebraic torus

Citation

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. https://projecteuclid.org/euclid.ant/1593482420


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