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UID:news825@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20211104T143247
DTSTART;TZID=Europe/Zurich:20190228T141500
SUMMARY:Number Theory Seminar: Yuri Bilu (Université de Bordeaux)
DESCRIPTION:The celebrated André-Oort conjecture about special point on Sh
 imura  varieties is now proved conditionally to the GRH in full generality
   and  unconditionally in many important special cases. In particular\, Pi
 la  (2011) proved it for products of modular curves\, adapting a method  p
 reviously developed by Pila and Zannier in the context of the  Manin-Mumfo
 rd conjecture. Unfortunately\, Pila's argument is  non-effective\, using t
 he Siegel-Brauer inequality. Since 2012 various special cases of the Andr
 é-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 v
 ariety" C^n and  will try to explain on some simple examples how the effec
 tive approach  of Kühne works. No previous knowledge about André-Oort co
 njecture is required\, I will give all the necessary background.
X-ALT-DESC: The celebrated André-Oort conjecture about special point on Sh
 imura  varieties is now proved conditionally to the GRH in full generality
   and  unconditionally in many important special cases. In particular\, Pi
 la  (2011) proved it for products of modular curves\, adapting a method  p
 reviously developed by Pila and Zannier in the context of the  Manin-Mumfo
 rd conjecture. Unfortunately\, Pila's argument is  non-effective\, using t
 he Siegel-Brauer inequality. <br /><br />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
  &quot\;Shimura variety&quot\; C^n and  will try to explain on some simple
  examples how the effective approach  of Kühne works. <br /><br />No prev
 ious knowledge about André-Oort conjecture is required\, I will give all 
 the necessary background. 
DTEND;TZID=Europe/Zurich:20190228T151500
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