On the motivic class of an algebraic group

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 $\{BG\}\{G\}\ne 1$ 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 $\{BA\}\ne 1$.

Final version

References in corpus (2)

• The Ekedahl Invariants for finite groups
• Motivic classes of some classifying stacks

Cited by in corpus (1)

• On the Mixed Tate property and the motivic class of the classifying stack of a finite group