Rigidity and unlikely intersections for formal groups

Laurent Berger (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

Let K be a p-adic field and let F and G be two formal groups of finite height over O_K. We prove that if F and G have infinitely many torsion points in common, then F=G. This follows from a rigidity result: any bounded power series that sends infinitely many torsion points of F to torsion points of F is an endomorphism of F.

Domaines: Théorie des nombres [math.NT]

Laurent Berger. Rigidity and unlikely intersections for formal groups. Acta Arithmetica, 2020, 195 (3), pp.305--312. ⟨10.4064/aa190523-5-12⟩. ⟨hal-01924930⟩