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Density of rational points on elliptic K3 surfaces

Fedor Bogomolov·Yuri Tschinkel
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Abstract

Let $X$ be a K3 surface defined over a number field $K$. Assume that $X$ admits a structure of an elliptic fibration or an infinite group of automorphisms. Then there exists a finite extension $K'/K$ such that the set of $K'$-rational points is Zariski dense in $X$.

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Fedor Bogomolov, Yuri Tschinkel. 1999-02-15. Density of rational points on elliptic K3 surfaces. https://arxiv.org/abs/math/9902092

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