A conjecture by Yves André and Frans Oort says that closed subvarieties of Shimura varieties that contain a Zariski dense subset of special points are subvarieties of Hodge type. We prove this in the case where the subvariety is a curve that contains infinitely many special points that lie in one Hecke orbit. Via work of Jürgen Wolfart, Paula Cohen and Gisbert Wüstholz, this result has an application to algebraicity of values of certain hypergeometric functions.
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