Spreading out perverse sheaves and Kashiwara's conjectures

Talk by Beat Zurbuchen

Date: 31.03.26  Time: 13.15 - 14.45  Room: Y27H25

Kashiwara's conjectures are deep statements about the cohomology of semisimple perverse sheaves, including the decomposition theorem and the Hard Lefschetz theorem. I will describe a new specialization method for perverse sheaves, which allows one to extend geometrically irreducible perverse sheaves from the generic fiber to a relatively perverse sheaf over an arbitrary quasi-excellent base scheme. This specialization method implies Kashiwara's conjectures for arithmetic complexes and implies stronger semisimplicity statements than were available before. The goal of this talk is to describe the extension theorem and its applications. This is work in progress.