Alessandro De Stefani: Frobenius Betti numbers and projective dimension

The Frobenius Betti numbers are numerical invariants that can be associated to a module M of finite length, over a local ring R of prime characteristic. In a way, they generalize the Hilbert–Kunz multiplicity and, when M is the residue field of R, they can be viewed as some kind of ‟asymptotic Betti numbers”. In this talk, we will discuss some motivations behind the study of these invariants, and some known results. We will present some new relations between the vanishing of these invariants and the projective dimension of a module of finite length. Time permitting, we will also discuss some related problems about Krull dimension of syzygies. This is joint work with Craig Huneke, and Luis Núñez-Betancourt.