Automorphisms of supersingular K3 surfaces and Salem polynomials

Abstract

We present a method to generate many automorphisms of a supersingular K3 surface in odd characteristic. As an application, we show that, if p is an odd prime less than or equal to 7919, then every supersingular K3 surface in characteristic p has an automorphism whose characteristic polynomial on the Néron-Severi lattice is a Salem polynomial of degree 22. For a supersingular K3 surface with Artin invariant 10, the same holds for odd primes less than or equal to 17389.

15 pages, results are improved

References in corpus (2)

• Automorphisms of elliptic $K3$ surfaces and Salem numbers of maximal degree
• Dynamics on supersingular K3 surfaces

Cited by in corpus (2)

• Dynamics on supersingular K3 surfaces and automorphisms of Salem degree 22
• Distribution of Mordell--Weil ranks of families of elliptic curves