Finiteness theorems for the Picard objects of an algebraic stack - Mathematics > Algebraic GeometryReport as inadecuate




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



Author: Sylvain Brochard

Source: https://arxiv.org/



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