The intersection matrices of X₀(p^r) and some applications

2022/10/17 by Debargha Banerjee, Banerjee, Debargha, Priyanka Majumder +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2210.08866

openalex publication_date 2022/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute intersection matrices for modular curves of the form X₀(p^r) with r ∈ \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 X₀(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 X₀(p^r) with r ∈ \3,4\ and obtain a bound on the stable Faltings height for those curves.

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