Non-thin rational points for elliptic K3 surfaces

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 surface...

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Bibliographic Details
Published in:arXiv.org 2024-04
Main Authors: Gvirtz-Chen, Damián, Mezzedimi, Giacomo
Format: Article
Language:English
Subjects:
Number theory
Online Access:Get full text
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Summary: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.
ISSN:2331-8422