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SUMMARY:The Andre-Oort conjecture via o-minimality
DTSTART;VALUE=DATE-TIME:20151028T133000Z
DTEND;VALUE=DATE-TIME:20151028T143000Z
DTSTAMP;VALUE=DATE-TIME:20200713T125356Z
UID:indico-event-897@indico.math.cnrs.fr
DESCRIPTION:« Return of the IHÉS Postdoc Seminar »\n\n \n\nAbstract: T
he Andre-Oort conjecture is an important problem in arithmetic geometry co
ncerning subvarieties of Shimura varieties. It attempts to characterise th
ose subvarieties V for which the special points lying on V constitute a Za
riski dense subset. When the ambient Shimura variety is the moduli space o
f principally polarised abelian varieties of dimension g (in which case\,
a special point is a point corresponding to the isomorphism class of a CM
abelian variety)\, the conjecture has been obtained by Pila and Tsimerman
via the so-called Pila-Zannier strategy\, reliant on the Pila-Wilkie count
ing theorem on o-minimal structures. In this talk\, we will outline the Pi
la-Zannier strategy\, providing some introduction to Shimura varieties and
Andre-Oort\, and explain the state of the art for the full conjecture. In
particular\, we will mention certain height bounds obtained jointly with
Orr.\n\nhttps://indico.math.cnrs.fr/event/897/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/897/
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