Equidistribution of special subvarieties. (Equidistribution de sous-variétés spéciales.) (French) Zbl 1099.11031

Authors’ abstract: For a Shimura-variety \(S\) the André-Oort conjecture says that for any subvariety \(Y\subset S\) the sub-Shimura-varieties \(S'\subset S\) which lie in \(Y\) are each contained in a finite set of maximal such \(S'\). The paper shows the analogous statement for \(S'\) for which the associated subgroup \(G'\subset G\) is not contained in any proper \(Q\)-parabolic. The proof uses a compactness statement for the associated probability measures, and relies heavily on the ergodic theory of unipotent flows.


11G18 Arithmetic aspects of modular and Shimura varieties
14G35 Modular and Shimura varieties
Full Text: DOI Euclid