Approximation in triangulated categories with partial Serre functors

Bregje Pauwels – 22 March 2023, 29 March 2023

Approximation, Serre duality and recollements are three major tools, theories really, used to study triangulated categories in algebraic geometry and representation theory. However, the existence of Serre duality is a very strong condition; the bounded derived category of a finite dimensional algebra satisfies Serre duality if and only if it has finite global dimension. Replacing Serre duality by the weaker notion of a partial Serre functor, we get a new tool which applies to any approximable category, and in particular to any ring.

In this talk, I will explain how these tools interact. I will briefly (and badly) introduce Neeman’s theory of approximation for triangulated categories, and show how approximability and Serre functors behave under recollements.