Bounding integral points on the Siegel modular variety A₂(2)

2020/07/28 by Josha Box, Box, Josha, Samuel Le Fourn +1
Mathematics · #14G05 #14K10 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2007.14422

openalex publication_date 2020/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine two explicit upper bounds for the stable Faltings height of principally polarised abelian surfaces over number fields corresponding to S-integral points on the Siegel modular variety A₂(2). One upper bound, using Runge's method, is uniform in S as long as |S|<3; the other, using Baker's method, is not uniform but allows |S|<10. Our application of a higher-dimensional Baker's method is completely explicit and improves upon the general case due to Levin.

Related

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• Integral points on coarse Hilbert moduli schemes
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• Integral points on the modular curves X₀(p)
• Smallness of Faltings heights of CM abelian varieties