Automorphisms of supersingular K3 surfaces and Salem polynomials

2015/03/16 by Shimada, Ichiro · 1 citation
#14J28 #14J50 #14Q10 #37B40 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1503.04517

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.

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