Special points on the product of two modular curves

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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.
hardcopy available at request to edix@univ-rennes1.fr LaTeX

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Algebraic Geometry, 14G35 (Primary) 11G18 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/150219

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/alg-geom/9610011
 http://arxiv.org/abs/alg-geom/9610011

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arXiv