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Commentarii Mathematici Helvetici

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Volume 91, Issue 4, 2016, pp. 705–719
DOI: 10.4171/CMH/400

Published online: 2016-10-24

Dynamics on supersingular K3 surfaces

Matthias Schütt[1]

(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