Foncteur de Picard d'un champ algébrique

Authors :: Sylvain Brochard
Institut de Mathématiques et de Modélisation de Montpellier (I3M)
Centre National de la Recherche Scientifique (CNRS)-Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM)
Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)
Source :: Mathematische Annalen, Mathematische Annalen, Springer Verlag, 2009, 343 (3), pp.541-602. ⟨10.1007/s00208-008-0282-8⟩
Publication Year :: 2009
Publisher :: HAL CCSD, 2009.
Abstract: 62 pages, in French; International audience; 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 X are geometrically normal. We study some examples of Picard functors of classical stacks. In an appendix, we review the lisse-étale cohomology of abelian sheaves on an algebraic stack.

Language :: French
ISSN :: 00255831 and 14321807
Database :: OpenAIRE
Journal :: Mathematische Annalen, Mathematische Annalen, Springer Verlag, 2009, 343 (3), pp.541-602. ⟨10.1007/s00208-008-0282-8⟩
Accession number :: edsair.doi.dedup.....d237237d48d84a73eaadd7bfe167c44d
Full Text :: https://doi.org/10.1007/s00208-008-0282-8⟩