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arXiv · 2108.11595

Potential density of projective varieties having an int-amplified endomorphism

Jia Jia·Takahiro Shibata·De-Qi Zhang
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Abstract

We consider the potential density of rational points on an algebraic variety defined over a number field $K$, i.e., the property that the set of rational points of $X$ becomes Zariski dense after a finite field extension of $K$. For a non-uniruled projective variety with an int-amplified endomorphism, we show that it always satisfies potential density. When a rationally connected variety admits an int-amplified endomorphism, we prove that there exists some rational curve with a Zariski dense forward orbit, assuming the Zariski dense orbit conjecture in lower dimensions. As an application, we prove the potential density for projective varieties with int-amplified endomorphisms in dimension $\leq 3$. We also study the existence of densely many rational points with the maximal arithmetic degree over a sufficiently large number field.

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Jia Jia, Takahiro Shibata, De-Qi Zhang. 2021-08-26. Potential density of projective varieties having an int-amplified endomorphism. https://arxiv.org/abs/2108.11595

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