# A surface in odd characteristic with discrete and non-finitely generated automorphism group

## TL;DR

This paper constructs a smooth projective surface over fields of odd characteristic with a discrete, non-finitely generated automorphism group, extending previous complex case results to positive characteristic.

## Contribution

It demonstrates the existence of such surfaces in odd characteristic fields, generalizing prior complex surface automorphism group results to positive characteristic.

## Key findings

- Automorphism group is discrete and not finitely generated
- Construction over algebraically closed fields of odd characteristic
- Extends complex surface automorphism results to positive characteristic

## Abstract

It was proved by Tien-Cuong Dinh and me that there is a smooth complex projective surface whose automorphism group is discrete and not finitely generated. In this paper, we will show that there is a smooth projective surface, birational to some K3 surface, such that the automorphism group is discrete and not finitely generated, over any algebraically closed field of odd characteristic except precisely an algebraic closure of the prime field.