Abstract

This paper concerns the relations between the relative Manin–Mumford conjecture and Pink’s conjecture on unlikely intersections in mixed Shimura varieties. The variety under study is the 4-dimensional Poincaré biextension attached to a universal elliptic curve. A detailed list of its special subvarieties is drawn up, providing partial verifications of Pink’s conjecture in this case, and two open problems are stated in order to complete its proof