29 April 2026 — Padova

Faithful highest weight perverse sheaves

Alessio Cipriani, University of Verona

Abstract

A heart of a bounded t-structure on a triangulated category is called faithful if there exists a realisation functor from the bounded derived category of the heart to the ambient triangulated category that is an equivalence. Using recent results of Bodzenta and Bondal, I will describe faithful highest weight hearts in terms of full exceptional sequences, and introduce an iterated notion of faithfulness. I will then focus on faithful perverse hearts, showing that they have bounded global dimension. Finally, I will prove that faithful perverse highest weight hearts can be characterised algebraically by the exactness of certain functors and geometrically by the vanishing of certain cohomology groups of pairwise links. This is joint work with Jon Woolf.