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SUMMARY:Unlikely intersections in Shimura varieties and abelian varieties 
 - Martin Orr (UCL)
DTSTART:20140121T161500Z
DTEND:20140121T171500Z
UID:TALK49621@talks.cam.ac.uk
CONTACT:James Newton
DESCRIPTION:The Manin-Mumford conjecture\, which is a theorem of Raynaud\,
  states that a curve of genus at least 2 in an abelian variety contains on
 ly finitely many torsion points. Analogues of this\, such as the André-Oo
 rt and Zilber-Pink conjectures\, have been stated for Shimura varieties in
  place of abelian varieties. In their most general form these imply many D
 iophantine results such as the Mordell-Lang conjecture. In this talk I wil
 l outline these conjectures and discuss one method of attacking them\, due
  to Pila and Zannier and using results from model theory. In particular I 
 will apply this method to a problem about curves in the moduli space of pr
 incipally polarised abelian varieties.
LOCATION:MR13
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