Reflexive dg categories in algebra and topology

Matt Booth (Imperial College London)

Friday 7th March 15:00-16:00 Maths 311B

Abstract

Reflexive dg categories were introduced by Kuznetsov and Shinder as common generalisations of smooth proper dg categories (for example, perfect complexes on a smooth projective variety). They are defined as the reflexive objects in the Morita homotopy category, but also admit a more down-to-earth definition in terms of their module categories. In this talk, I'll explain what a reflexive dg category is, give a couple of ways of thinking about them, and then give some families of examples, mostly arising from algebraic geometry, representation theory, and algebraic topology. This is based on work in progress joint with Isambard Goodbody and Sebastian Opper.

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