论文标题
希尔伯特模块化表面上的相互交集
Just-likely intersections on Hilbert modular surfaces
论文作者
论文摘要
在本文中，我们证明了与某些希尔伯特模块化表面的曲线有关的相交理论结果。具体而言，我们表明，给定两条适当的曲线C，d参数化的Abelian表面具有实际乘法，即产品CXD中的一组点（X，Y），其表面由X和Y彼此参数为参数为X d中的Zariski致密，从而证明了一个非常相似的交叉分裂的想法。我们还计算了在适当的ABELIAN表面的适当的p驱动等菌液下的恶质高度的变化，其在特征p全球磁场上具有实际乘积。
In this paper, we prove an intersection-theoretic result pertaining to curves in certain Hilbert modular surfaces in positive characteristic. Specifically, we show that given two appropriate curves C,D parameterizing abelian surfaces with real multiplication, the set of points (x,y) in the product CxD with surfaces parameterized by x and y isogenous to each other is Zariski dense in C x D, thereby proving a case of a just-likely intersection conjecture. We also compute the change in Faltings height under appropriate p-power isogenies of abelian surfaces with real multiplication over characteristic p global fields.
