Quasi-F-split and Hodge-Witt
Algebraic Geometry
2023-12-04 v1
Abstract
We study an analogy between quasi-F-split and Hodge-Witt. In particular, we show that the fiber product of an F-split scheme and a quasi-F-split scheme is quasi-F-split and, in converse, if the fiber product is quasi-F-split then one of the factors is F-split and the other is quasi-F-split. This is an analogy of Ekedahl's theorem, which says the fiber product of an ordinary scheme and a Hodge-Witt scheme is Hodge Witt and if the product is Hodge-Witt then one of the factors is ordinary and the other is Hodge-Witt. As an application, we show that, for any prime p, there is a klt Fano fourfold in characteristic p which is not quasi-F-split.
Cite
@article{arxiv.2312.00682,
title = {Quasi-F-split and Hodge-Witt},
author = {Fuetaro Yobuko},
journal= {arXiv preprint arXiv:2312.00682},
year = {2023}
}
Comments
16 pages