论文标题
Dynamique Analytique sur $ \ mathbf {z} $。 II：Écart统一的EntreLattès等人猜想De Bogomolov-fu-tschinkel
Dynamique analytique sur $\mathbf{Z}$. II : Écart uniforme entre Lattès et conjecture de Bogomolov-Fu-Tschinkel
论文作者
论文摘要
我们证明，在$ \ \ \ mathbf {\ bar Q} $上相关的两个动态系统的相互能量（或相交产物）是在下面统一的，并推断出了bogomolov-fu-tschinkel的猜想的证明，并推断出两种不合格的图像的数量来证明。 $ \ mathbf {c} $通过标准形态对投影线的界限均匀地界定。该证明至关重要地依赖于$ \ mathbf {z} $的伯科维奇空间理论，以及原始参数，允许从中心估计（在一个微不足道的字段上）获得全局估计。
We prove that the mutual energy (or the intersection product in the sense of Arakelov theory) of two dynamical systems associated to Lattès morphisms over $\mathbf{\bar Q}$ is uniformly bounded below and deduce a proof of a conjecture of Bogomolov-Fu-Tschinkel: the number of common images of torsion points of two non-isomorphic elliptic curves over $\mathbf{C}$ by a standard morphism to the projective line is uniformly bounded. The proof crucially relies on the theory of Berkovich spaces over $\mathbf{Z}$ and on an original argument allowing to obtain a global estimate from a central estimate (over a trivially valued field).
