# Good reduction of K3 Surfaces in equicharacteristic p

## TL;DR

This paper extends the criteria for good reduction of K3 surfaces in characteristic p, demonstrating that under certain conditions, good reduction can be descended over purely inseparable extensions.

## Contribution

It generalizes the Neron-Ogg-Shafarevich criterion for K3 surfaces to the equicharacteristic p>0 setting, using descent techniques.

## Key findings

- Good reduction descends over purely inseparable extensions for certain varieties.
- Extension of Neron-Ogg-Shafarevich criterion to characteristic p>0.
- Applicable to smooth, proper varieties with no non-trivial vector fields.

## Abstract

We show that for smooth and proper varieties over local fields with no non-trivial vector fields, good reduction descends over purely inseparable extensions. We use this to extend the Neron-Ogg-Shafarevich criterion for K3 surfaces to the equicharacteristic $p>0$ case.