论文标题
不太可能，只是椭圆曲线高维家族的交叉点
Unlikely and just likely intersections for high dimensional families of elliptic curves
论文作者
论文摘要
在模块化曲线的n倍产物中，给定了两个品种V，W，我们肯定地回答了一个问题（由Shou-wu Zhang的AIM组提出），介绍了V中某个点的hecke the hecke the Points的集合是否在V中是密集的。我们需要在V，v，divise n diviss ancuts cur的情况下进行一些假设，但在v and是一个diviss and divise and We是一个cur的假设。我们还研究了在不太可能的交叉点的情况下，我们的假设的必要性，并表明与例外相反，有限场上高维空间中的两条曲线可以无限地与Hecke翻译相交。
Given two varieties V,W in the n-fold product of modular curves, we answer affirmatively a question (formulated by Shou-Wu Zhang's AIM group) on whether the set of points in V that are Hecke translations of some point on W is dense in V. We need to make some (necessary) assumptions on the dimensions of V,W but for instance, when V is a divisor and W is a curve, no further assumptions are needed. We also examine the necessity of our assumptions in the case of unlikely intersections and show that, contrary to exceptions, two curves in a high dimensional space over a finite field can intersect infinitely often up to Hecke translations.
