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CATEGORIES:Number Theory Seminar
SUMMARY:Unlikely Intersections in certain families of abel
ian varieties and the polynomial Pell equation - F
abrizio Barroero (University of Manchester)
DTSTART;TZID=Europe/London:20160524T141500
DTEND;TZID=Europe/London:20160524T151500
UID:TALK65658AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/65658
DESCRIPTION:Given n independent points on the Legendre family
of elliptic curves of equation Y^2=X(X-1)(X-t) wit
h coordinates algebraic over Q(t)\, we will see th
at there are at most finitely many specializations
of c such that two independent relations hold bet
ween the n points on the specialized curve. This f
its in the framework of the so-called Unlikely Int
ersections. We will then see an higher-dimensional
analogue of this result and explain how it applie
s to the problem of studying the solvability of th
e (almost-)Pell equation in polynomials.\nThis is
joint work with Laura Capuano.
LOCATION:MR13\, Centre for Mathematical Sciences
CONTACT:G. Rosso
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