Submission date: 2 December 2011.

Abstract:

The 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 verications of Pink's conjecture in this case, and two open problems are stated in order to complete its proof.

Mathematics Subject Classification: 11G18, 14K12.

Keywords and phrases:

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