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

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 \(\{B\!A\}\neq 1\).


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


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