English

Foncteur de Picard d'un champ alg\'ebrique

Algebraic Geometry 2009-09-18 v1

Abstract

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.

Keywords

Cite

@article{arxiv.0711.4545,
  title  = {Foncteur de Picard d'un champ alg\'ebrique},
  author = {Sylvain Brochard},
  journal= {arXiv preprint arXiv:0711.4545},
  year   = {2009}
}
R2 v1 2026-06-21T09:48:19.333Z