Special points on the product of two modular curves

1996/10/11 by Bas Edixhoven, Edixhoven, Bas · 1 citation
Mathematics · #14G35 (Primary) 11G18 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #alg-geom #math.AG #msc:11G18 #msc:14G35

paper · pdf · doi:10.48550/arxiv.alg-geom/9610011

hardcopy available at request to [email protected] LaTeX

arxiv created 1996/10/11 · arxiv updated 2009/11/30

Abstract

We prove, assuming the Generalized Riemann Hypothesis for imaginary quadratic fields, that irreducible curves in the product of two modular curves that contain infinitely many complex multiplication points are either a Hecke correspondence or a fibre for one of the two projections. This gives evidence for a conjecture of Oort that says that irreducible components of the Zariski closure of a set of CM points in a Shimura variety are sub Shimura varieties.

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• Unlikely intersections in Shimura varieties and beyond: a survey

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