# Mathematical Sciences Research Institute

Home » Unlikely intersections in semi-abelian schemes.

# Seminar

Unlikely intersections in semi-abelian schemes. April 18, 2014 (04:10 PM PDT - 05:30 PM PDT)
Location: 891 Evans Hall
Speaker(s) Daniel Bertrand (Université de Paris VI (Pierre et Marie Curie))
Description No Description

Video
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.