Ordinary reduction of K3 surfaces

TL;DR

This paper proves that for any K3 surface over a number field, there exists a finite extension where the surface has ordinary reduction at almost all non-archimedean places, except for a density zero set.

Contribution

It establishes the existence of a finite extension making a K3 surface have ordinary reduction at nearly all places, advancing understanding of reduction properties of K3 surfaces.

Findings

Existence of a finite extension with ordinary reduction at almost all places.

Reduction properties hold outside a density zero set of places.

Advances the understanding of reduction behavior of K3 surfaces.

Abstract

Let X be a K3 surface over a number field K. We prove that there exists a finite algebraic field extension L/K such that X has ordinary reduction at every non-archimedean place of L outside a density zero set of places.