论文标题
$ x_0（p^r）$和某些应用的交叉矩阵
The intersection matrices of $X_0(p^r)$ and some applications
论文作者
论文摘要
我们计算$ x_0（p^r）$的模块化曲线的相交矩阵与$ r \ in \ {3,4 \} $ in \ {3,4 \} $，并且作为一个应用程序，我们计算了Arakelov的自我交流的渐近表达式 多于。该计算对于理解Bogolomov猜想的有效版本对于模块化曲线的稳定型号$ x_0（p^r）$的有效版本将是有用的。
We compute intersection matrices for modular curves of the form $X_0(p^r)$ with $r \in \{3,4\}$ and as an application, we compute an asymptotic expression for the Arakelov self-intersection number of the relative dualizing sheaf of Edixhoven's minimal regular model for the modular curve $X_0(p^r)$ over $\qq$ with $r$ as above. This computation will be useful to understand an effective version of the Bogolomov conjecture for the stable models of modular curves $X_0(p^r)$ with $r \in \{3,4\}$ and obtain a bound on the stable Faltings height for those curves.
