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arXiv · 1503.04517

Automorphisms of supersingular K3 surfaces and Salem polynomials

Ichiro Shimada
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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 N\'eron-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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Ichiro Shimada. 2015-03-16. Automorphisms of supersingular K3 surfaces and Salem polynomials. https://arxiv.org/abs/1503.04517

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