Dynamics on supersingular K3 surfaces

Abstract

For any odd characteristic p=2 mod 3, we exhibit an explicit automorphism on the supersingular K3 surface of Artin invariant one which does not lift to any characteristic zero model. Our construction builds on elliptic fibrations to produce a closed formula for the automorphism's characteristic polynomial on second cohomology, which turns out to be an irreducible Salem polynomial of degree 22 with coefficients varying with p.

12 pages, 3 figures; v2: main result improved to Salem degree 22

Cited by in corpus (3)

• Elliptic fibrations on K3 surfaces and Salem numbers of maximal degree
• Automorphisms of supersingular K3 surfaces and Salem polynomials
• Dynamics on supersingular K3 surfaces and automorphisms of Salem degree 22