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

Clozel, Laurent; Ullmo, Emmanuel

Ann. Math. (2) 161, No. 3, 1571-1588 (2005).

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.

Reviewer: Gerd Faltings (Bonn)

MSC:

11G18	Arithmetic aspects of modular and Shimura varieties
14G35	Modular and Shimura varieties

Keywords:

André-Oort conjecture; Shimura varieties