Number Theory Seminar

Speaker: Lars Kühne (KU)

Title: Equidistribution in families of Abelian varieties

Abstract: I will discuss analogues of classical conjectures in diophantine geometry in the "relative" setting of families of abelian varieties. These conjectures are the Manin-Mumford conjecture, the Bogomolov conjecture, and the equidistribution conjecture, all of which have been proven in the nineties. In the last decade, there has been some progress on their "relative" analogues (e.g., by Masser-Zannier, DeMarco-Mavraki), which are however still far from being settled completely. I will then describe a work-in-progress proof of the "relative" equidistribution conjecture -- and indicate how this should help to prove a relative analogue of the Bogomolov conjecture in a few select cases.