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arXiv · 1610.07341

Fundamental gerbes

Niels Borne·Angelo Vistoli
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Abstract

For a class of affine algebraic groups $\mathcal C$ over a field, we define the notions of $\mathcal C$-fundamental gerbe of a fibered category, generalizing what we had done in arXiv:1204.1260 for finite group schemes. We give sufficient conditions on $\mathcal C$ implying that a fibered category $X$ over $κ$ satisfying mild hypotheses admits a Nori $\mathcal C$-fundamental gerbe. We show that these are verified in particular by the classes of virtually abelian and virtually unipotent group schemes. In the second situation, under a properness condition on $X$, we give a tannakian interpretation of the resulting gerbe.

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Niels Borne, Angelo Vistoli. 2017-06-20. Fundamental gerbes. https://doi.org/10.2140/ant.2019.13.531

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