Reduction of Kummer surfaces modulo 2 in the non-supersingular case

TL;DR

This paper characterizes when Kummer surfaces associated with abelian surfaces over fields of characteristic 2 have good reduction, providing explicit criteria and constructions for algebraic space and scheme models.

Contribution

It offers necessary and sufficient conditions for good reduction of Kummer surfaces in characteristic 2, including explicit constructions of models.

Findings

Criteria for good reduction in characteristic 2

Equivalence of algebraic space and scheme models for reduction

Explicit construction of models

Abstract

We obtain necessary and sufficient conditions for the good reduction of Kummer surfaces attached to abelian surfaces with non-supersingular reduction when the residue field is perfect of characteristic 2. In this case, good reduction with an algebraic space model is equivalent to good reduction with a scheme model, which we explicitly construct.