Automorphisms of Salem degree $22$ on supersingular K3 surfaces of higher Artin invariant

We give a short proof that every supersingular K3 surface (except possibly in characteristic $2$ with Artin invariant $\sigma = 10$) has an automorphism of Salem degree $22$. In particular an infinite subgroup of the automorphism group does not lift to characteristic zero. The proof relies on the case $\sigma = 1$ and the cone conjecture for K3 surfaces.

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Received 1 November 2016

Accepted 14 August 2017

Published 16 November 2018