In this paper we extend the generalized algebraic fundamental group constructed in Esnault and Hogadi, (Trans. Amer. Math. Soc. 364(5) (2012), 2429–2442) to general fibered categories using the language of gerbes. As an application we obtain a Tannakian interpretation for the Nori fundamental gerbe defined in Borne and Vistoli (J. Algebraic Geom. (2014), S1056–3911, 00638-X) for nonsmooth non-pseudo-proper algebraic stacks.
Algebraic and Nori fundamental gerbes / Tonini, Fabio; Zhang, Lei. - In: JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU. - ISSN 1474-7480. - ELETTRONICO. - (2019), pp. 0-43. [10.1017/S147474801700024X]
Algebraic and Nori fundamental gerbes
Tonini, Fabio;
2019
Abstract
In this paper we extend the generalized algebraic fundamental group constructed in Esnault and Hogadi, (Trans. Amer. Math. Soc. 364(5) (2012), 2429–2442) to general fibered categories using the language of gerbes. As an application we obtain a Tannakian interpretation for the Nori fundamental gerbe defined in Borne and Vistoli (J. Algebraic Geom. (2014), S1056–3911, 00638-X) for nonsmooth non-pseudo-proper algebraic stacks.
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Tannakian Gerbes.pdf
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