Finiteness theorems for the Picard objects of an algebraic stack
Algebraic Geometry
2011-12-19 v3
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.
Cite
@article{arxiv.0904.1166,
title = {Finiteness theorems for the Picard objects of an algebraic stack},
author = {Sylvain Brochard},
journal= {arXiv preprint arXiv:0904.1166},
year = {2011}
}
Comments
29 pages. Final version, including the remarks of the referee. To appear in Adv. Math