Arakelov self-intersection numbers of minimal regular models of modular curves X0(p2)

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 X0(p2) over Q. The computation of the self-intersection numbers are used to prove an effective version of the Bogolomov conjecture for the semi-stable models of modular curves X0(p2) and obtain a bound on the stable Faltings height for those curves in a companion article (Banerjee and Chaudhuri in Isr J Math, 2020).