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arXiv · 2210.08866

The intersection matrices of $X_0(p^r)$ and some applications

Debargha Banerjee·Priyanka Majumder·Chitrabhanu Chaudhuri
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Abstract

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.

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Debargha Banerjee, Priyanka Majumder, Chitrabhanu Chaudhuri. 2022-10-17. The intersection matrices of $X_0(p^r)$ and some applications. https://arxiv.org/abs/2210.08866

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