Universiteit Leiden Mathematisch Instituut
Geometry Seminar

Friday, 23 May 2008, 16:00–17:00, room TBA

Sylvain Brochard: Picard functor of an algebraic stack

Abstract:

The Picard functor of a scheme, classifying invertible sheaves on it, has been studied extensively in the 60's. However, the work of Giraud, Deligne, Mumford and Artin gave birth in the 70's to the notion of an /algebraic stack/, which generalizes that of a scheme. The following question arises then: does the Picard functor of an algebraic stack behave like that of a scheme. We will explain how the study of deformations of invertible sheaves allows us to prove that the Picard functor is representable by an algebraic space (under suitable hypothesis). We will also try to see, through a few examples, what is the effect on the Picard scheme, when we modify a scheme by adding some "stacky structure".