UCalgary Algebra and Number Theory Seminar: Tangli Ge

I will talk about a unification of two bounded height results around abelian varieties. The first is Silverman’s specialization theorem, which states for an abelian scheme A/C with no fixed part over a curve C, that the set of points on C where the generic Mordell—Weil group fails to specialize injectively has bounded height. The second is by Habegger in an abelian variety: a suitable subvariety intersected with all torsion cosets up to complementary dimension gives a set of bounded height. I will take the point of view from unlikely intersections and discuss the key idea of the arithmetic part of the proof by homomorphism approximations using Ax—Schanuel results.