Linear Equations in Singular Moduli

Yuri Bilu; Lars Kuhne

doi:10.48550/arXiv.1712.04027

Linear Equations in Singular Moduli

Yuri Bilu
, Lars Kuhne^*

^*Corresponding author for this work

Institute of Algebra, Number Theory and Discrete Mathematics

Universite de Bordeaux

Research output: Contribution to journal › Article › Research › peer review

Abstract

We establish an effective version of the André-Oort conjecture for linear subspaces of $Y(1)^n_{\mathbb{C}} \approx \mathbb{A}_{\mathbb{C}}^n$. This gives the first effective nontrivial results of André-Oort type for higher-dimensional varieties in products of modular curves.

Original language	English
Pages (from-to)	7617-7643
Number of pages	27
Journal	International Mathematics Research Notices
Volume	2020
Issue number	21
E-pub ahead of print	14 Sept 2018
DOIs	https://doi.org/10.48550/arXiv.1712.04027 https://doi.org/10.1093/imrn/rny216
Publication status	Published - 1 Nov 2020

ASJC Scopus subject areas

General Mathematics

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title = "Linear Equations in Singular Moduli",

abstract = "We establish an effective version of the Andr{\'e}-Oort conjecture for linear subspaces of \$Y(1)\textasciicircum{}n\_\{\textbackslash{}mathbb\{C\}\} \textbackslash{}approx \textbackslash{}mathbb\{A\}\_\{\textbackslash{}mathbb\{C\}\}\textasciicircum{}n\$. This gives the first effective nontrivial results of Andr{\'e}-Oort type for higher-dimensional varieties in products of modular curves.",

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doi = "10.48550/arXiv.1712.04027",

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AU - Kuhne, Lars

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N2 - We establish an effective version of the André-Oort conjecture for linear subspaces of $Y(1)^n_{\mathbb{C}} \approx \mathbb{A}_{\mathbb{C}}^n$. This gives the first effective nontrivial results of André-Oort type for higher-dimensional varieties in products of modular curves.

AB - We establish an effective version of the André-Oort conjecture for linear subspaces of $Y(1)^n_{\mathbb{C}} \approx \mathbb{A}_{\mathbb{C}}^n$. This gives the first effective nontrivial results of André-Oort type for higher-dimensional varieties in products of modular curves.

UR - https://www.scopus.com/pages/publications/85097449850

U2 - 10.48550/arXiv.1712.04027

DO - 10.48550/arXiv.1712.04027

M3 - Article

AN - SCOPUS:85097449850

SN - 1073-7928

VL - 2020

SP - 7617

EP - 7643

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 21

ER -

Linear Equations in Singular Moduli

Abstract

ASJC Scopus subject areas

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