Non-thin rational points for elliptic K3 surfaces

Damián Gvirtz-Chen, Giacomo Mezzedimi

Published 2024-04-10Version 1

We prove that elliptic K3 surfaces over a number field which admit a second elliptic fibration satisfy the potential Hilbert property. Equivalently, the set of their rational points is not thin after a finite extension of the base field. Furthermore, we classify those families of elliptic K3 surfaces over an algebraically closed field which do not admit a second elliptic fibration.