Nonarchimedean dynamical systems and formal groups

Laurent Berger (1, 2)

1 IUF - Institut universitaire de France
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

We confirm an observation of Lubin concerning families of $p$-adic power series that commute under composition. We prove that under certain conditions, there is a formal group such that the power series in the family are either endomorphisms of this group, or at least semi-conjugate to endomorphisms of this group.

Domaines: Théorie des nombres [math.NT]

Laurent Berger. Nonarchimedean dynamical systems and formal groups. Proceedings of the American Mathematical Society, 2019, 147, ⟨10.1090/proc/1440⟩. ⟨hal-01476629⟩