# Enriques surfaces with finite automorphism group in positive characteristic

## TL;DR

This paper classifies Enriques surfaces with finite automorphism groups in positive characteristic, describing their moduli and realizing all types over prime fields, extending known complex results.

## Contribution

It provides a classification of such surfaces in positive characteristic, highlighting differences from complex cases and describing their moduli spaces.

## Key findings

- Classification matches complex case except in small characteristics
- Complete description of moduli spaces of these surfaces
- Realization of all types over finite and rational fields

## Abstract

We classify Enriques surfaces with smooth K3 cover and finite automorphism group in arbitrary positive characteristic. The classification is the same as over the complex numbers except that some types are missing in small characteristics. Moreover, we give a complete description of the moduli of these surfaces. Finally, we realize all types of Enriques surfaces with finite automorphism group over the prime fields $\mathbb{F}_p$ and $\mathbb{Q}$ whenever they exist.