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arXiv · 1710.10915

Arakelov Self-intersection numbers of minimal regular models of modular curves $X_0(p^2)$

Debargha Banerjee·Diganta Borah·Chitrabhanu Chaudhuri
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Abstract

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 $X_0(p^2)$ over $\mathbb{Q}$. The computation of the self-intersection numbers are used to prove effective Bogolomov conjecture for the semi-stable models of modular curves $X_0(p^2)$ and obtain a bound on the stable Faltings height for those curves in a companion article arXiv:1802.06968.

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Debargha Banerjee, Diganta Borah, Chitrabhanu Chaudhuri. 2019-07-22. Arakelov Self-intersection numbers of minimal regular models of modular curves $X_0(p^2)$. https://doi.org/10.1007/s00209-020-02480-1

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