Ordinary K3 surfaces over a finite field
Algebraic Geometry
2018-06-19 v2 Number Theory
Abstract
We give a description of the category of ordinary K3 surfaces over a finite field in terms of linear algebra data over Z. This gives an analogue for K3 surfaces of Deligne's description of the category of ordinary abelian varieties over a finite field, and refines earlier work by N.O. Nygaard and J.-D. Yu. Our main result is conditional on a conjecture on potential semi-stable reduction of K3 surfaces over p-adic fields. We give unconditional versions for K3 surfaces of large Picard rank and for K3 surfaces of small degree.
Cite
@article{arxiv.1711.09225,
title = {Ordinary K3 surfaces over a finite field},
author = {Lenny Taelman},
journal= {arXiv preprint arXiv:1711.09225},
year = {2018}
}