Learning seminar on Perverse Sheaves

Homological theories on smooth algebraic varieties enjoy many nice properties (notably duality results). Intersection cohomology and perverse sheaves have been introduced at the beginning of the 80’s by Goresky-MacPherson and Beilinson-Bernstein-Deligne-Gabber in order to provide a good homological framework for singular varieties. The aim of this seminar is to study these notions in depth, with a view towards geometry and arithmetic. Except where indicated we aim for each topic to be covered over the course of one week, which translates to one talk of (roughly) two hours.
There are plenty of references on the subject, but we choose to focus on the following :

• [BBDG18] A. Beilinson, J. Bernstein, P. Deligne, O. Gabber "Faisceaux pervers", Société mathématique de France (2018)
• [PS08] C. A.M. Peters and J. H.M. Steenbrink, "Mixed Hodge Structures", Springer-Verlag (2008)
• [KW01] R. Kiehl and R. Weissauer. , "Weil Conjectures, Perverse Sheaves and l’adic Fourier Transform", Springer-Verlag (2001)
• [dCM09] M. de Cataldo and L. Migliorini. , "The decomposition theorem, perverse sheaves and the topology of algebraic maps", Bulletin of the American Mathematical Society (2009)

Schedule for the talks

Place: IMJ-PRG, Room 15-25-502