23 research outputs found
Dynamics on supersingular K3 surfaces
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.Comment: 12 pages, 3 figures; v2: main result improved to Salem degree 2
Distribution of Mordell--Weil ranks of families of elliptic curves
We discuss the distribution of Mordell--Weil ranks of the family of elliptic
curves where are
coprime polynomials that parametrize the projective smooth conic
and are elements from . In our
previous papers we discussed certain special cases of this problem and in this
article we complete the picture by proving the general results.Comment: 28 page