Unlikely intersections in families of abelian varieties
Heilbronn Number Theory Seminar
16th May 2018, 4:00 pm – 5:00 pm
Howard House, 4th Floor Seminar Room
Two varieties whose dimensions do not sum up to at least the dimension of the ambient space should not intersect. This guiding philosophy, usually called "unlikely intersection", led several authors to propose conjectures about subvarieties of commutative algebraic groups and of Shimura varieties. After a brief introduction about these problems, I will talk about about results for curves in families of abelian varieties, obtained in collaboration with F. Barroero. The proof of these theorems uses a method introduced by Pila and Zannier and combines results coming from o-minimality with some Diophantine ingredients.