## Algebra & Number Theory

### On the motivic class of an algebraic group

Federico Scavia

#### 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
Revised: 16 July 2019
Accepted: 19 December 2019
First available in Project Euclid: 30 June 2020

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

#### 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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