The Nori fundamental gerbe of a fibered category

2012/04/05 by Borne, Niels, Vistoli, Angelo · 4 citations
#14A20 #14H30 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1204.1260

Abstract

We give a condition that ensures that a fibered category over a field admits a universal morphism to a profinite gerbe. This fundamental gerbe generalizes both Nori's fundamental group scheme and Deligne's relative fundamental groupoid. Using a simplified notion of essentially finite bundle, we also give a tannakian construction. As an application, we show how the fundamental gerbe enables to formulate a version of Grothendieck's section conjecture in arbitrary characteristic. We then study various natural quotients of the fundamental gerbe.

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• Fundamental group schemes of globally F-regular varieties
• F-divided bundles on normal F-finite schemes
• The étale fundamental group and F-divided sheaves in characteristic p>0
• A co-operational bivariant theory derived from cohomology operations

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