Séminaire d'Arithmétique

Cartier duality, character sheaves, and generic vanishing

by Gabriel Ribeiro (École Polytechnique)

CMLS, École Polytechnique

CMLS, École Polytechnique


Since Green and Lazarsfeld's seminal work, generic vanishing theorems have influenced many fields ranging from birational geometry to analytic number theory. In this talk, I will present a new generic vanishing theorem for holonomic D-modules, that may shed new light on both of these worlds. Following ideas of Laumon, I'll explain how "character sheaves" play the role of topologically trivial line bundles and construct their moduli space based on a stacky version of Cartier duality.