论文标题
假设乘法变性的模块化曲线产物中的Zilber-Pink
Zilber-Pink in a product of modular curves assuming multiplicative degeneration
论文作者
论文摘要
我们证明了在$ y（1）^n $中的Zilber-pink猜想，其Zariski在$（\ Mathbb {p}^1）^n $中封闭的Zariski封闭均通过点$（\ infty，\ ldots，\ infty），超出了Habegger和Pila的不对称状况。我们的证明是基于遵循安德烈（André）的G功能方法的高度绑定的。主要的新颖性是，我们在许多非架构的地方对G功能的评估之间的关系进行了利用。
We prove the Zilber--Pink conjecture for curves in $Y(1)^n$ whose Zariski closure in $(\mathbb{P}^1)^n$ passes through the point $(\infty, \ldots, \infty)$, going beyond the asymmetry condition of Habegger and Pila. Our proof is based on a height bound following André's G-functions method. The principal novelty is that we exploit relations between evaluations of G-functions at unboundedly many non-archimedean places.
