Unlikely intersections of curves with algebraic subgroups in semiabelian varieties

Abstract

AbstractLet G be a semiabelian variety and $$C$$ C a curve in G that is not contained in a proper algebraic subgroup of G. In this situation, conjectures of Pink and Zilber imply that there are at most finitely many points contained in the so-called unlikely intersections of $$C$$ C with subgroups of codimension at least 2. In this note, we establish this assertion for general semiabelian varieties over $$\overline{\mathbb {Q}}$$ Q ¯ . This extends results of Maurin and Bombieri, Habegger, Masser, and Zannier in the toric case as well as Habegger and Pila in the abelian case.