AI 中文总结
该论文研究定义在ℂₚ上的光滑曲线C与模子簇Y₀(n)交轨迹的p进等分布性，给出等分布成立的条件，证明对应交集合非离散，并给出等分布不成立的典型例子。
AI 中文摘要
设C是定义在ℂₚ上且具有不可约约化的光滑曲线，我们研究C与模子簇Y₀(n)的交轨迹。若曲线C避开两个坐标均具有超奇异约化的点，或取序列Y₀(aₙ)且aₙ被p整除的程度递增，则这些轨迹等分布到解析化的唯一典范点Cᵇᵉʳₖ。若两个条件均不满足，我们预期等分布不成立，并给出一组被认为具有典型性的例子。我们还研究集合C∩∪ₙY₀(n)的聚点，证明该集合恒非离散。
英文摘要
Let $C\subset X(1)\times X(1)$ be a smooth curve defined over $\mathbb{C}_p$ with irreducible reduction. We study the intersection loci of $C$ with the modular subvarieties $Y_0(n)$. If the curve $C$ avoids points where both coordinates have supersingular reduction, or if a sequence $Y_0(a_n)$ is taken where the numbers $a_n$ have increasing divisibility by $p$, then these loci equidistribute to the unique canonical point of the analytification, $C^\text{Berk}$. If neither condition is satisfied, we expect equidistribution to fail and give a family of examples whose behaviour is believed to be typical. We also study the accumulation points of the set $C\cap\bigcup_nY_0(n)$ and show that this set is always non-discrete.
Comments32 pages
