Laura Capuano, Oxford

PDL C401
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 almostPell equations in polynomials, generalising some previous results due to Masser and Zannier. This is a joint work with Fabrizio Barroero (Basel).