English

Relative semiampleness in mixed characteristic

Algebraic Geometry 2021-06-14 v1

Abstract

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 characteristic. In the process of the proof, we provide a generalisation 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.

Keywords

Cite

@article{arxiv.2106.06088,
  title  = {Relative semiampleness in mixed characteristic},
  author = {Jakub Witaszek},
  journal= {arXiv preprint arXiv:2106.06088},
  year   = {2021}
}
R2 v1 2026-06-24T03:04:50.502Z