Abstract Daniel Schäppi

Title: Tensor categories arising in algebraic geometry

Abstract: Varieties, schemes, group schemes, and various generalizations thereof are often studied via an associated tensor category (the category of quasi-coherent sheaves or the category of representations). From a result of Lurie we know that for many algebro-geometric objects, passage to quasi-coherent sheaves gives an embedding in the 2-category of tensor categories. This raises several natural questions: can we characterize the image of this embedding purely in the language of tensor categories? Is this embedding compatible with various geometric constructions (for example, fiber products)? In my talk I will outline how generalizations of the Tannakian formalism can be used to provide some answers to these questions.

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