A. Cipriani

collaborators

4 papers

math.RT2026

Indecomposable extensions of perverse sheaves over a closed stratum

Alessio Cipriani

Given a topologically stratified space $X$ , we develop a categorical framework for extensions of perverse sheaves over a closed stratum $S$ . We introduce the notion of $S$ -small ex…

math.RT2026

Faithful perversities

Alessio Cipriani, Jon Woolf

We show that the faithful highest weight hearts in an algebraic triangulated category are the serially faithful glued hearts, equivalently the hearts containing a dual pair of full…

math.RT2026

Highest weight categories and stability conditions

Alessio Cipriani, Jon Woolf

Highest weight categories are an abstraction of the representation theory of semisimple Lie algebras introduced by Cline, Parshall and Scott in the late 1980s. There are by now man…

math.RT2025

Serre functor and $P$ -objects for perverse sheaves on $P^{n}$

Lukas Bonfert, Alessio Cipriani

We show that the inverse Serre functor for the constructible derived category $D_{c}^{b} (P^{n})$ is given by the $P$ -twist at the simple perv…

Indecomposable extensions of perverse sheaves over a closed stratum

Faithful perversities

Highest weight categories and stability conditions

Serre functor and P-objects for perverse sheaves on Pn

Serre functor and $P$ -objects for perverse sheaves on $P^{n}$