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

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.

arXiv comment40 pages, 4 figures

References in corpus (2)

• Self-intersection of the relative dualizing sheaf on modular curves $X_1(N)$
• Semi-stable models of modular Curves $X_0(p^2)$ and some arithmetic applications

Cited by in corpus (1)

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