Location:

00.003 Spiegelgasse 1

## Number Theory Seminar: Yuri Bilu (Université de Bordeaux)

**Towards effective André-Oort (after Kühne et al.) **

The celebrated André-Oort conjecture about special point on Shimura varieties is now proved conditionally to the GRH in full generality and unconditionally in many important special cases. In particular, Pila (2011) proved it for products of modular curves, adapting a method previously developed by Pila and Zannier in the context of the Manin-Mumford conjecture. Unfortunately, Pila's argument is non-effective, using the Siegel-Brauer inequality.

Since 2012 various special cases of the André-Oort conjecture has been proved effectively, most notably in the work of Lars Kühne. In my talk I will restrict to the case of the "Shimura variety" C^n and will try to explain on some simple examples how the effective approach of Kühne works.

No previous knowledge about André-Oort conjecture is required, I will give all the necessary background.

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