Champs alg\'ebriques et foncteur de Picard

TL;DR

This thesis explores algebraic Champs and the Picard functor, with key results published in a subsequent article, focusing on algebraic stacks and their cohomological properties.

Contribution

It presents new results on algebraic Champs and the Picard functor, strengthening previous findings and providing a comprehensive reference for related cohomological proofs.

Findings

Results on the Picard functor of algebraic stacks

Strengthened previous theorems in algebraic geometry

Clarified proofs related to smooth-étale cohomology on stacks

Abstract

This text is my thesis, defended in June 2007, in the status it was at this time. The most important results are contained in the article "Foncteur de Picard d'un champ alg\'ebrique" to appear in "Mathematische Annalen" (see the preprint arXiv:0711.4545). In the article, some results have been added, and some previous results have been strengthened. However, the proofs of the results contained in the appendix (concerning the smooth-\'etale cohomology on an algebraic stack) have been removed. The thesis is only put on the ArXiv to provide a more lasting reference than my webpage for these proofs.