# Relative Manin-Mumford in additive extensions

**Harry Schmidt **(University of Basel)

Abstract: We will discuss the relative Manin-Mumford conjecture for families of two dimensional commutative algebraic groups. These will depend on one complex parameter λ and we are especially interested in the case of an additive extension of the Legendre family *E*_{λ}. We then have an exact sequence 0 → G_{a }→ *G*_{λ} → E_{λ }→ 0 where G_{a} is the additive group (C, +). In this context the relative Manin-Mumford conjecture states that the intersection of a curve in *G*_{λ} with the set of torsion points is at most finite unless it is contained in a smaller family of algebraic subgroups in *G*_{λ. } It is possible to prove this by following the strategy employed by Masser and Zannier in their proof of the relative Manin-Mumford conjecture for the product of two Legendre families.