Commentarii Mathematici Helvetici
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Published online: 2016-10-24
Dynamics on supersingular K3 surfacesMatthias Schütt (1) Leibniz-Universität Hannover, Germany
For any odd characteristic $p\equiv 2$ 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 $p$.
Keywords: K3 surface, automorphism, elliptic fibration, Salem number, supersingular, liftability
Schütt Matthias: Dynamics on supersingular K3 surfaces. Comment. Math. Helv. 91 (2016), 705-719. doi: 10.4171/CMH/400