Finitistic dimension and derived categories

Jeremy Rickard (University of Bristol)

Wednesday 26th October, 2022 16:00-17:00 Maths 311B


The Finitistic Dimension Conjecture (FDC) is a long open conjecture about homological properties of finite dimensional algebras that has gradually assumed greater importance as it has been realised that it implies many other conjectures in the field. A few years ago I showed that if the derived category of an algebra is generated in a certain sense by injective modules (and we know no examples where it isn’t) then the FDC would follow for that algebra. The question of whether the derived category is generated by injective modules makes sense for general rings, although in this generality there are (a few) counterexamples. In this talk I will discuss some results and open questions about these ideas. I will not assume any technical knowledge of derived categories.

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