Automorphisms of Salem degree 22 on supersingular K3 surfaces of higher Artin invariant

TL;DR

The paper proves that most supersingular K3 surfaces have automorphisms with Salem degree 22, highlighting a difference from characteristic zero cases and relying on the cone conjecture.

Contribution

It provides a short proof that supersingular K3 surfaces (except possibly in characteristic 2 with Artin invariant 10) have Salem degree 22 automorphisms, extending understanding of their automorphism groups.

Findings

Supersingular K3 surfaces generally have Salem degree 22 automorphisms.

Automorphisms of Salem degree 22 do not lift to characteristic zero.

The proof uses the case of Artin invariant 1 and the cone conjecture.

Abstract

We give a short proof that every supersingular K3 surface (except possibly in characteristic $2$ with Artin invariant $\sigma=10$) has an automorphism of Salem degree 22. In particular an infinite subgroup of the automorphism group does not lift to characteristic zero. The proof relies on the case $\sigma=1$ and the cone conjecture for K3 surfaces.