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International conference "Arithmetic as Geometry: Parshin Fest"
November 27, 2012 12:30, Moscow, Steklov Mathematical Institute of RAS


Special points on curves in products of modular curves

G. Wüstholz

Swiss Federal Institute of Technology Zurich, Department of Mathematics



Abstract: 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.

Language: English


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