Potential density under int-amplified endomorphisms

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Let KK be a number field and let XX be a projective variety defined over KK. A variety satisfies potential density if there is a finite field extension K⊆LK \subseteq L such that XL(L)X_L(L) is Zariski dense in XLX_L, where XL≔X×Spec⁡KSpec⁡LX_L \coloneqq X \times_{\operatorname{Spec} K} \operatorname{Spec} L. An endomorphism of XX is int-amplified if it is int-amplified in the sense used in the paper.

Potential density under int-amplified endomorphisms. If XX admits an int-amplified endomorphism, then XX satisfies potential density.

This conjecture links arithmetic potential density with the geometry and dynamics of projective varieties admitting int-amplified endomorphisms. The parser supplies no evidence that it has been resolved, so its status remains open.

References

Primary source

Jia Jia, Takahiro Shibata and De-Qi Zhang, “Potential density of projective varieties having an int-amplified endomorphism”, arXiv:2108.11595 (2021).

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