On the motivic class of an algebraic group. (English) Zbl 1454.14116

Scavia, Federico

Algebra Number Theory 14, No. 4, 855-866 (2020).

Summary: 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 \(\{BG\}\neq\{G\}^{-1}\) 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 \(B\!A\) is stably rational and \(\{B\!A\}\neq 1\).

MSC:

14L15	Group schemes
14D23	Stacks and moduli problems
14C35	Applications of methods of algebraic \(K\)-theory in algebraic geometry

Keywords:

motivic class; Grothendieck ring of stacks; classifying stack; algebraic torus

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