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University of Cambridge > Talks.cam > Number Theory Seminar > Unlikely Intersections in certain families of abelian varieties and the polynomial Pell equation

## Unlikely Intersections in certain families of abelian varieties and the polynomial Pell equationAdd to your list(s) Download to your calendar using vCal - Fabrizio Barroero (University of Manchester)
- Tuesday 24 May 2016, 14:15-15:15
- MR13, Centre for Mathematical Sciences.
If you have a question about this talk, please contact G. Rosso. Given n independent points on the Legendre family of elliptic curves of equation Y^2=X(X-1)(X-t) with coordinates algebraic over Q(t), we will see that there are at most finitely many specializations of c such that two independent relations hold between the n points on the specialized curve. This fits in the framework of the so-called Unlikely Intersections. We will then see an higher-dimensional analogue of this result and explain how it applies to the problem of studying the solvability of the (almost-)Pell equation in polynomials. This is joint work with Laura Capuano. This talk is part of the Number Theory Seminar series. ## This talk is included in these lists:- All CMS events
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