论文标题
具有最大算术程度的点的Zariski密度
Zariski density of points with maximal arithmetic degree
论文作者
论文摘要
鉴于在一个数字字段上的投影变化上具有主要的理性自图，我们可以在理性点定义算术程度。众所周知，任何点的算术程度都小于或等于第一个动力学程度。在本文中，我们表明，对于具有最大算术程度（即其算术程度等于第一个动力学程度）的$ \ overline {\ mathbb q} $ - 用于投影品种的自我态度的理性点。对于婚姻品种和Abelian品种，我们表明，在足够大的字段上，存在最大算术程度的密集程度。我们还对附录中的Kawaguchi和Silverman的结果进行了概括。
Given a dominant rational self-map on a projective variety over a number field, we can define the arithmetic degree at a rational point. It is known that the arithmetic degree at any point is less than or equal to the first dynamical degree. In this article, we show that there are densely many $\overline{\mathbb Q}$-rational points with maximal arithmetic degree (i.e. whose arithmetic degree is equal to the first dynamical degree) for self-morphisms on projective varieties. For unirational varieties and abelian varieties, we show that there are densely many rational points with maximal arithmetic degree over a sufficiently large number field. We also give a generalization of a result of Kawaguchi and Silverman in the appendix.
