Abstract
For a class of affine algebraic groups over a field , we define the notion of -fundamental gerbe of a fibered category, generalizing what we did for finite group schemes in a 2015 paper.
We give necessary and sufficient conditions on implying that a fibered category over satisfying mild hypotheses admits a Nori -fundamental gerbe. We also give a tannakian interpretation of the gerbe that results by taking as the class of virtually unipotent group schemes, under a properness condition on .
Finally, we prove a general duality result, generalizing the duality between group schemes of multiplicative type and Galois modules, that yields a construction of the multiplicative gerbe of multiplicative type which is independent of the previous theory, and requires weaker hypotheses. This gives a conceptual interpretation of the universal torsor of Colliot-Thélène and Sansuc.
Citation
Niels Borne. Angelo Vistoli. "Fundamental gerbes." Algebra Number Theory 13 (3) 531 - 576, 2019. https://doi.org/10.2140/ant.2019.13.531
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