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ALGEBRAIC AND NORI FUNDAMENTAL GERBES

Part of: Algebraic geometry: Foundations

Published online by Cambridge University Press:  07 July 2017

Fabio Tonini  and
Lei Zhang
Fabio Tonini
Affiliation:
Freie Universität Berlin, FB Mathematik und Informatik, Arnimallee 3, Zimmer 112A, 14195 Berlin, Deutschland (tonini@zedat.fu-berlin.de; l.zhang@fu-berlin.de)
Lei Zhang
Affiliation:
Freie Universität Berlin, FB Mathematik und Informatik, Arnimallee 3, Zimmer 112A, 14195 Berlin, Deutschland (tonini@zedat.fu-berlin.de; l.zhang@fu-berlin.de)
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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.

Keywords

algebraic geometrycategory theoryhomological algebraalgebraic topology

MSC classification

Primary: 14A15: Schemes and morphisms 14A20: Generalizations (algebraic spaces, stacks) 14A05: Relevant commutative algebra
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 18 , Issue 4 , July 2019 , pp. 855 - 897
Copyright
© Cambridge University Press 2017 

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Footnotes

This work was supported by the European Research Council (ERC) Advanced Grant 0419744101 and the Einstein Foundation.

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