论文标题
CM点和Hecke轨道的P-ADIC分布。 I.汇合到高斯点
p-Adic distribution of CM points and Hecke orbits. I. Convergence towards the Gauss point
论文作者
论文摘要
我们研究了椭圆曲线在$ \ mathbb {c} _p $上的模量空间上CM点的渐近分布，这是基础内态环的歧视性。与复杂情况相反，我们表明没有统一的分布。在本文中，我们表征了所有判别因子序列，相应的CM点会收敛于Berkovich仿射线的高斯点。我们还为Hecke Orbits提供了类似的表征。在同伴论文中，我们表征了CM点和Hecke Orbits的所有剩余极限度量。
We study the asymptotic distribution of CM points on the moduli space of elliptic curves over $\mathbb{C}_p$, as the discriminant of the underlying endomorphism ring varies. In contrast with the complex case, we show that there is no uniform distribution. In this paper we characterize all the sequences of discriminants for which the corresponding CM points converge towards the Gauss point of the Berkovich affine line. We also give an analogous characterization for Hecke orbits. In the companion paper we characterize all the remaining limit measures of CM points and Hecke orbits.
