Relative Manin-Mumford for Abelian Varieties

With an eye or two towards applications to Pell's equation and to Davenport's work on integration of algebraic functions, Umberto Zannier and I have recently characterised torsion points on a fixed algebraic curve in a fixed abelian scheme of dimension bigger than one (when all is defined over the algebraic numbers): there are at most finitely many points provided the natural obstacles are absent. I sketch the proof as well as the applications.