Foncteur de Picard d'un champ algébrique

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.

References in corpus (3)

• Revêtements étales et groupe fondamental (SGA 1)
• Complete moduli for families over semistable curves
• Champs algébriques et foncteur de Picard

Cited by in corpus (11)

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• Geometric Langlands in prime characteristic
• Morphisms of 1-motives defined by line bundles
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• Twisted stable maps to tame Artin stacks
• Higher-dimensional study of extensions via torsors
• An embedding problem for finite local torsors over twisted curves
• Triangulated categories of relative 1-motives
• Building Data for Stacky Covers
• Mirror of Orbifold Singularities in the Hitchin Fibration: the case $({\text{SL}}_n,{\text{PGL}}_n)$
• Vanishing of Brauer groups of moduli stacks of stable curves