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arXiv · 1802.06968

Semi-stable models of modular Curves $X_0(p^2)$ and some arithmetic applications

Debargha Banerjee·Chitrabhanu Chaudhuri
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Abstract

In this paper, we compute the semi-stable models of modular curves $X_0(p^2)$ for odd primes $p > 3$ and compute the Arakelov self-intersection numbers of the relative dualising sheaves for these models. We give two arithmetic applications of our computations. In particular, we give an effective version of the Bogomolov conjecture following the strategy outlined by Zhang and find the stable Faltings heights of the arithmetic surfaces corresponding to these modular curves.

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Debargha Banerjee, Chitrabhanu Chaudhuri. 2020-01-09. Semi-stable models of modular Curves $X_0(p^2)$ and some arithmetic applications. https://doi.org/10.1007/s11856-021-2107-3

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