| Résume | We report on some Hodge theoretic criteria characterizing special subvarieties of Shimura varieties, and a weak form of the André-Oort Problem, characterizing special subvarieties which contain sufficiently many special subvarieties of dimension at least one. It turns out that already in the case of curves on surfaces the non-smoothness of Hecke translates plays an interesting role, and is related to other open conjectures in Algebraic geometry. |
