# zbMATH — the first resource for mathematics

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.

##### MSC:
 11G18 Arithmetic aspects of modular and Shimura varieties 14G35 Modular and Shimura varieties
##### Keywords:
André-Oort conjecture; Shimura varieties
Full Text: