Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



The Nori fundamental gerbe of a fibered category

Authors: Niels Borne and Angelo Vistoli
Journal: J. Algebraic Geom. 24 (2015), 311-353
Published electronically: September 18, 2014
MathSciNet review: 3311586
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Abstract: We extend Nori's theory of the fundamental group scheme to a theory of the fundamental gerbe, which applies to schemes, algebraic stacks, and more general fibered categories, even in the absence of a rational point. We give a Tannakian interpretation of the fundamental gerbe in terms of essentially finite bundles, extending Nori's correspondence for complete varieties with a rational point. We also show how our formalism allows a natural formulation of Grothendieck's Section Conjecture in arbitrary characteristic.

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Niels Borne
Affiliation: Laboratoire Paul Painlevé, Université de Lille, U.M.R. CNRS 8524, U.F.R. de Mathématiques, 59 655 Villeneuve d’Ascq Cedex, France

Angelo Vistoli
Affiliation: Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy

Received by editor(s): June 14, 2012
Received by editor(s) in revised form: January 29, 2013
Published electronically: September 18, 2014
Additional Notes: The first author was supported in part by the Labex CEMPI (ANR-11-LABX-0007-01) and Anr ARIVAF (ANR-10-JCJC 0107). The second author was supported in part by the PRIN project “Geometria delle varietà algebriche e dei loro spazi di moduli” from MIUR
Article copyright: © Copyright 2014 University Press, Inc.
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society