论文标题
Silverman-Tate的高度不等式的动态版本
A dynamical version of Silverman-Tate's height inequality
论文作者
论文摘要
在论文《莫尔德尔·兰格》（Mordell-lang）的论文中，他们使用了西尔弗曼·泰特（Silverman-Tate）的身高不平等，并提供了同样的证明，并且可以使用卡地亚分区，从而使结构上的结构化熟食化熟食。但是，他们的证明利用了Hironaka的定理解决了奇异性的解决，这对于积极特征的领域未知。我们尝试稍微修改他们的想法，使用爆炸代替Hironaka定理，以使证据有效地有效，可以定义高度，并将任何正常的准标记品种作为基础。我们在动态系统的更一般建立中工作。作为应用程序，我们证明了Silverman专业定理的某些变体，并在较高维度的基础上具有受限的假设。
In the paper "Uniformity of Mordell-Lang" by Vesselin Dimitrov, Philipp Habegger and Ziyang Gao (arXiv:2001.10276), they use Silverman-Tate's Height Inequality and they give a proof of the same which makes use of Cartier divisors and hence drops the flatness assumption of structure morphisms of compactified abelian schemes. However, their proof makes use of Hironaka's theorem on resolution of singularities which is unknown for fields of positive characteristic. We try to slightly modify their ideas, use blow-ups in place of Hironaka's theorem to make the proof effective for any fields with product formula where heights can be defined and any normal quasi-projective variety as a base. We work in the more general set up of dynamical systems. As an application we prove certain variant of Silverman's Specialization Theorem with restricted hypotheses in higher dimensional bases.
