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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