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Tannaka Duality for Geometric Stacks

Jacob Lurie
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Abstract

We show that, under appropriate hypothesis, the groupoid of maps from S to an an algebraic stack X can be identified with a category of tensor functors from coherent sheaves on X to coherent sheaves on S. As an application, we show that if S is a proper variety over the field of complex numbers, then every ``analytic'' map from S to X is ``algebraic''.

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Jacob Lurie. 2005-03-23. Tannaka Duality for Geometric Stacks. https://arxiv.org/abs/math/0412266

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