Аннотация:
In the talk we report on a recent work on the André–Oort conjecture
in the special case that the Shimura variety is a product of modular curves.
André has shown that there are only finitely many special points.
In a recent Annals paper, Kühne has given an alternative proof which is
effective. We shall explain how the result can be obtained in a more systematic and
therefore more elegant way. Linear forms in logarithms and the analytic
subgroup theorem are the main ingredients for the proof. Our approach opens the view for
trying to deal also with more general Shimura varieties.