We show that a nef line bundle on a proper scheme over an excellent base is semiample if and only if it is semiample after restricting to characteristic zero and to positive characteristics. In the process of the proof, we provide a generalization to mixed characteristic of the fact that the perfection of the Picard functor in positive characteristic is a stack in groupoids for the h-topology.
Duke Math. J.
173(9):
1631-1675
(15 June 2024).
DOI: 10.1215/00127094-2023-0053
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