Is Andre-Oort conjecture expected to hold for complex analytic topology? If yes, do the recent results on abelian type Shimura varieties cover this case? 


Sorry for my ignorance, but several references seem to deal with Zariski topology. Thanks.


Edit - Let $S$ be an infinite subset of special points Zariski dense in a Shimura variety $Sh$. Can we characterise when it is also dense in the analytic topology? Say, characterisation in terms of tori giving rise to the special points in $S$. 



Andre-Oort for conjecture
The André-Oort conjecture is about the special points of a Shimura variety that lie on a subvariety — it claims that if there is a Zariski dense set of those points, then the subvariety is special as well. (No need to know what special means, here.) 


Since the Zariski topology is coarser than the complex analytic one, it would be a stronger assumption that there is a dense set of points, and the resulting theorem would be weaker. 


On the other hand, it is known (but non-trivial) that the special points are dense in a special variety for the complex analytic topology.


