Some invariants related to the finitistic dimension
The finitistic dimension of Artin algebras is notoriously hard to understand. In this talk, we’ll discuss an attempt to pin it down in terms of a new invariant, defined more generally over sufficiently nice Noetherian rings. Originally meant to model the finitistic dimension of Iwanaga-Gorenstein rings, it unexpectedly also gave the correct answer for commutative local Noetherian rings, Artin algebras of radical square zero, and (due to recent results of Ringel and Sen) Nakayama algebras. Given time, we’ll also discuss links with the notion of “finitistic” Auslander algebras recently introduced by Marczinzik.