Dynamics on supersingular K3 surfaces and automorphisms of Salem degree 22

TL;DR

This paper constructs explicit automorphisms of Salem degree 22 on supersingular K3 surfaces in characteristic p ≡ 3 mod 4, showing these automorphisms cannot be lifted to characteristic zero models.

Contribution

It provides a systematic method to produce maximal Salem degree automorphisms on supersingular K3 surfaces in specific characteristics, highlighting their unique properties.

Findings

Explicit automorphisms of Salem degree 22 are constructed for all primes p ≡ 3 mod 4.

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

The method applies systematically across the specified primes.

Abstract

In this note we exhibit explicit automorphisms of maximal Salem degree 22 on the supersingular K3 surface of Artin invariant one for all primes p congruent 3 mod 4 in a systematic way. Automorphisms of Salem degree 22 do not lift to any characteristic zero model.