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Theses

Champs algébriques et foncteur de Picard

Abstract : The Picard functor of a scheme 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. We study in this thesis the Picard functor of an algebraic stack and generalize in this context some results that are well-known for the case of schemes. In particular we study the following points: deformation theory of invertible sheaves, representability of the Picard functor, construction and properness of the connected component of the identity, separation properties. We illustrate the thesis with some examples. We were also led to review the lisse-etale cohomology of an algebraic stack and proved a lot of technical details about it, put together in an appendix.
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https://tel.archives-ouvertes.fr/tel-00492445
Contributor : Sylvain Brochard <>
Submitted on : Thursday, June 24, 2010 - 6:14:25 PM
Last modification on : Thursday, January 7, 2021 - 4:23:57 PM
Long-term archiving on: : Monday, September 27, 2010 - 10:56:12 AM

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  • HAL Id : tel-00492445, version 1

Citation

Sylvain Brochard. Champs algébriques et foncteur de Picard. Mathématiques [math]. Université Rennes 1, 2007. Français. ⟨tel-00492445⟩

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