Dynamics on supersingular K3 surfaces
Algebraic Geometry
2016-11-14 v2 Dynamical Systems
Number Theory
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.
Cite
@article{arxiv.1502.06923,
title = {Dynamics on supersingular K3 surfaces},
author = {Matthias Schuett},
journal= {arXiv preprint arXiv:1502.06923},
year = {2016}
}
Comments
12 pages, 3 figures; v2: main result improved to Salem degree 22