Martin Orr

Height bounds for very unlikely intersections in abelian varieties using G-functions

A special case of the Zilber-Pink conjecture, proved by
Habegger and Pila, states that a generic curve C in an abelian variety A
has only finitely many "unlikely intersections", that is, intersections
of C with subgroups of A of codimension at least 2. One important
ingredient in the proof is a bound for the height of these intersection
points. In this talk, I will discuss a new method of proving such a
height bound for intersections with subgroups of large codimension
("very unlikely intersections"), using ideas of Bombieri and André about
G-functions. A benefit of this method is that it is in principle effective.