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Universal geometric tensor categories

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If you have a question about this talk, please contact Dr Ignacio Lopez Franco.

Many objects in algebraic geometry have an associated tensor category of quasi-coherent sheaves. This category contains rich information about the geometry of the object in question. In fact, a large class of objects can be completely recovered from its category of coherent sheaves. This works particularly well for Adams stacks (these include classical geometric objects such as projective varieties): for Adams stacks, passage to the tensor category of quasi-coherent sheaves gives a 2-fully faithful pseudofunctor.

In my talk I will explain how the notion of a geometric tensor category gives a characterization of the image of this pseudofunctor, and how we can construct universal geometric tensor categories.

This talk is part of the Category Theory Seminar series.

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