Ampleness criteria for algebraic spaces
In this paper are proven three criteria for the ampleness of invertible sheaves over an algebraic space X over a field k: the cohomological criterion, Nakai-Moishezon's and Grauert's. The proof of the Nakai- Moishezon criterion follows the same way as for schemes, and we deduce the cohomological criterion from this one avoiding the use of points and Zariski topology used in EGA III. The proof of Grauert's criterion is based on a gometric interpretation of multiplicity due to Ramanujam.
scientific article; zbMATH DE number 3880850