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CATEGORIES:Number Theory Seminar
SUMMARY:Unlikely intersections in families of abelian vari
eties and some polynomial Diophantine equations -
Laura Capuano (University of Oxford)
DTSTART;TZID=Europe/London:20171017T143000
DTEND;TZID=Europe/London:20171017T153000
UID:TALK76321AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/76321
DESCRIPTION:What makes an intersection likely or unlikely? A s
imple dimension count shows that two varieties of
dimension r and s are non "likely" to intersect if
r < codim s\, unless there are some special geome
trical relations among them. A series of conjectur
es due to Bombieri-Masser-Zannier\, Zilber and Pin
k rely on this philosophy. After a small survey on
these problems\, I will speak about a joint work
with F. Barroero (Basel) in this framework in the
special case of curves in families of abelian vari
eties. This gives also applications to the study o
f the solvability of the so called "almost-Pell" e
quations\, generalising some results due to Masser
and Zannier.
LOCATION:MR13
CONTACT:Beth Romano
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