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arXiv · 1409.5404

Motivic classes of some classifying stacks

Daniel Bergh
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Abstract

We prove that the class of the classifying stack $B PGL_n$ is the multiplicative inverse of the class of the projective linear group $PGL_n$ in the Grothendieck ring of stacks for $n = 2$ and $n = 3$ under mild conditions on the base field $k$. In particular, although it is known that the multiplicativity relation $\{T\} = \{S\}\cdot\{PGL_n\}$ does not hold for all $PGL_n$-torsors $T \to S$, it holds for the universal $PGL_n$-torsors for said $n$.

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Daniel Bergh. 2014-09-18. Motivic classes of some classifying stacks. https://doi.org/10.1112/jlms%2Fjdv059

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