Bas Edixhoven, Andrei Yafaev
Published 2001-05-29, updated 2004-02-17Version 2
A conjecture by Yves Andre 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 Juergen Wolfart, Paula Cohen and Gisbert Wuestholz, this result has an application to algebraicity of values of hypergeometric functions.
Comments: 25 pages, published version
Journal: Ann. of Math. (2), Vol. 157 (2003), no. 2, 621--645
Hecke orbits on Shimura varieties of Hodge type
De Rham $F$-gauges and Shimura varieties
A guide to the reduction modulo p of Shimura varieties
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