Seminar

Given a "non-special" section of a semi-abelian scheme over a curve, the relative Manin-Mumford conjecture (RMM) asserts that its image W meets only finitely many torsion curves. I will explain how a relative version of the points constructed (in a Kummer theoretical setting) by the organizer of this seminar  provide ``very special" examples of infinite intersection. However, the corresponding curves W recover a "normally special" status, when viewed in the setting of Pink's conjecture on mixed Shimura varieties. Furthermore, these sections form the only counterexample to the standard version of RMM for semi-abelian surfaces. These are joint results with B. Edixhoven, and with D. Masser, A. Pillay and U. Zannier.