Foncteur de Picard d'un champ algébrique

Details Foncteur de Picard d'un champ algébrique Foncteur de Picard d'un champ algébrique

2007-11-28

arxiv.org/abs/0711.4545v1

Math. Ann. Volume 343, Number 3 / mars 2009, pages 541-602.

Mathematics

Algebraic Geometry

Scientific paper

10.1007/s00208-008-0282-8

In this article we study the Picard functor and the Picard stack of an algebraic stack. We give a new and direct proof of the representability of the Picard stack. We prove that it is quasi-separated, and that the connected component of the identity is proper when the fibers of the stack are geometrically normal. We study some examples of Picard functors of classical stacks. In an appendix, we review the lisse-etale cohomology of abelian sheaves on an algebraic stack.

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