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 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.

The Nori fundamental gerbe of a fibered category

VISTOLI, ANGELO
2015

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 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.
Settore MAT/03 - Geometria
Fundamantal group schemes, gerbes, fibered categories.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11384/55844
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