Rational Points on Elliptic K3 Surfaces of Quadratic Twist Type

verfasst von

Zhizhong Huang

Abstract

In studying rational points on elliptic K3 surfaces of the form $$\begin{equation∗} f(t)y^2=g(x), \end{equation∗}$$ where f, g are cubic or quartic polynomials (without repeated roots), we introduce a condition on the quadratic twists of two elliptic curves having simultaneously positive Mordell-Weil rank. We prove a necessary and sufficient condition for the Zariski density of rational points by using this condition, and we relate it to the Hilbert property. Applying to surfaces of Cassels-Schinzel type, we prove unconditionally that rational points are dense both in Zariski topology and in real topology.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Typ

Artikel

Journal

Quarterly Journal of Mathematics

Band

72

Seiten

755-772

Anzahl der Seiten

18

ISSN

0033-5606

Publikationsdatum

09.2021

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Mathematik (insg.)

Elektronische Version(en)

https://arxiv.org/abs/1806.07869 (Zugang: Offen)
https://doi.org/10.1093/qmath/haaa044 (Zugang: Geschlossen)