Linear Equations in Singular Moduli

2017/12/11 by Yuri Bilu, Bilu, Yuri, Lars Kühne +1 · 2 citations
Mathematics · Physics and Astronomy · #11G18 (primary) #11G50 #11R37 #14G35 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1712.04027

openalex publication_date 2017/12/11 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28

Abstract

We establish an effective version of the André-Oort conjecture for linear subspaces of Y(1)ⁿ_ℂ ≈ \mathbbA_ℂⁿ. Apart from the trivial examples provided by weakly special subvarieties, this yields the first algebraic subvarieties in a Shimura variety of dimension > 1 whose CM-points can be (theoretically) determined.

Cited by

• Modular Zilber-Pink for geometrically generic varieties
• Some effective estimates for André-Oort in Y(1)ⁿ

Related

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• Canonical Heights on Shimura Varieties and the André-Oort Conjecture
• Bounded equidistribution of special subvarieties I
• A characterization of special subvarieties in orthogonal Shimura varieties
• A proof of the Andre-Oort conjecture for A_g