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Unlikely intersections in families of abelian varieties and generalized Pell equations in polynomials 

Laura Capuano, Oxford
Tuesday, November 21, 2017 - 11:00am to 12:00pm
PDL C-401

Let A be an abelian scheme over a smooth irreducible curve S and let C be an irreducible curve inside A, where everything is defined over a number field k. We prove that if C is not contained in a proper subgroup scheme of A, then it intersects at most finitely many irreducible components of flat subgroup schemes of codimension at least 2. This is a special case of a more general conjecture of Pink and fits in the so called problems of unlikely intersections. This result has also some applications in the study of the almost-Pell equations in polynomials, generalising some previous results due to Masser and Zannier. This is a joint work with Fabrizio Barroero (Basel).

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