TY - JOUR

T1 - Dynamics on supersingular K3 surfaces

AU - Schütt, Matthias

N1 - Funding Information: Funding by ERC StG 279723 (SURFARI) is gratefully acknowledged. The isotrivial fibrations first came up in discussions with Tetsuji Shioda to whom I am greatly indebted. I benefitted greatly from comments by Simon Brandhorst, Hélène Esnault, Keiji Oguiso and the anonymous referee. Thanks also to Víctor González-Alonso and Jaap Top for discussions on the subject.

PY - 2016/10/24

Y1 - 2016/10/24

N2 - For any odd characteristic p=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.

AB - For any odd characteristic p=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.

KW - Automorphism

KW - Elliptic fibration

KW - K3 surface

KW - Lift-ability

KW - Salem number

KW - Supersingular

UR - http://www.scopus.com/inward/record.url?scp=84994689492&partnerID=8YFLogxK

U2 - 10.48550/arXiv.1502.06923

DO - 10.48550/arXiv.1502.06923

M3 - Article

AN - SCOPUS:84994689492

VL - 91

SP - 705

EP - 719

JO - Commentarii mathematici Helvetici

JF - Commentarii mathematici Helvetici

SN - 0010-2571

IS - 4

ER -