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CATEGORIES:Number Theory Seminar
SUMMARY:Unlikely intersections in Shimura varieties and ab
elian varieties - Martin Orr (UCL)
DTSTART;TZID=Europe/London:20140121T161500
DTEND;TZID=Europe/London:20140121T171500
UID:TALK49621AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/49621
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 only finitely ma
ny torsion points. Analogues of this\, such as the
AndrĂ©-Oort and Zilber-Pink conjectures\, have bee
n stated for Shimura varieties in place of abelian
varieties. In their most general form these imply
many Diophantine results such as the Mordell-Lang
conjecture. In this talk I will outline these con
jectures and discuss one method of attacking them\
, due to Pila and Zannier and using results from m
odel theory. In particular I will apply this metho
d to a problem about curves in the moduli space of
principally polarised abelian varieties.
LOCATION:MR13
CONTACT:James Newton
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