Vlad Serban (Vienna), p-adic unlikely intersections and applications
It was conjectured by Manin and Mumford and established by work of Raynaud and many others that subvarieties of a semi-abelian variety G which intersect more than finitely many torsion points of G must contain a translate of a semi-abelian subvariety of G. We present a p-adic version of this result for formal subschemes of a p-divisble formal Lie group G. We then outline some applications, including to non-vanishing for certain two-variable p-adic L-functions.