Finiteness theorems for the Picard objects of an algebraic stack

Abstract

We prove some finiteness theorems for the Picard functor of an algebraic stack, in the spirit of SGA 6, exp. XII and XIII. In particular, we give a stacky version of Raynaud's relative representability theorem, we give sufficient conditions for the existence of the torsion component of the Picard functor, and for the finite generation of the Neron-Severi groups or of the Picard group itself. We give some examples and applications. In an appendix, we prove the semicontinuity theorem for a (non necessarily tame) algebraic stack.

29 pages. Final version, including the remarks of the referee. To appear in Adv. Math

References in corpus (2)

• Quotients by Groupoids
• Foncteur de Picard d'un champ algébrique

Cited by in corpus (3)

• On the Picard group scheme of the moduli stack of stable pointed curves
• Cohomology and base change for algebraic stacks
• Vanishing of Brauer groups of moduli stacks of stable curves