Alessio Cipriani - University of Verona
16 May 2023
Perverse sheaves: introduction and examples.
Abstract: Perverse sheaves on topologically stratified
spaces were introduced by Beilinson, Bernstein and Deligne as hearts
of t-structures on the constructible derived category. In this talk,
I will introduce the formalism of BBD and I will explain some
important features of categories of perverse sheaves. I will then
present some examples, including the case of perverse sheaves on the
complex projective line stratified by $\mathbb C$ and a point with
respect to different perversities.
24 May 2023
On the global dimension of perverse sheaves.
Abstract: Any category of p-perverse sheaves on a
topologically stratified space with finitely many strata, each
with fundamental group, is a module category over a finite
dimensional algebra. That is, one can associate to a topologically
stratified space with finitely many strata, each with finite
fundamental group, a family of finite dimensional algebras indexed
by the perversity.
In this talk, we investigate the global dimension of such family of
algebras by using HRS-tilting and silting theory.