2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150219We 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 LaTeXAlgebraic Geometry14G35 (Primary) 11G18 (Secondary)text