activity
20202026
collaborators

6 papers

math.RT2026

Indecomposable extensions of perverse sheaves over a closed stratum

Alessio Cipriani

Given a topologically stratified space , we develop a categorical framework for extensions of perverse sheaves over a closed stratum . We introduce the notion of -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.RT2025

Serre functor and -objects for perverse sheaves on

Lukas Bonfert, Alessio Cipriani

We show that the inverse Serre functor for the constructible derived category is given by the -twist at the simple perv…

math.RT2024

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.RT2023

Wall And Chamber Structure For A Special Biserial Algebra Coming From Perverse Sheaves on

Alessio Cipriani, Martina Lanini

We describe the wall and chamber structure of a special biserial algebra whose module category is equivalent to the category of (middle) perverse sheaves on the complex projective…

math.RT2020

Perverse sheaves and finite-dimensional algebras

Alessio Cipriani, Jon Woolf

Let be a topologically stratified space, be any perversity on , and be a field. We show that the category of -perverse sheaves on , constructible with respect…