# Lubin's conjecture for full $p$-adic dynamical systems

Abstract : We give a short proof of a conjecture of Lubin concerning certain families of $p$-adic power series that commute under composition. We prove that if the family is \emph{full} (large enough), there exists a Lubin-Tate formal group such that all the power series in the family are endomorphisms of this group. The proof uses ramification theory and some $p$-adic Hodge theory.
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-01295254
Contributor : Laurent Berger <>
Submitted on : Wednesday, March 30, 2016 - 4:14:55 PM
Last modification on : Thursday, April 4, 2019 - 10:18:05 AM

### Identifiers

• HAL Id : hal-01295254, version 1
• ARXIV : 1603.03631

### Citation

Laurent Berger. Lubin's conjecture for full $p$-adic dynamical systems. Publications Mathématiques de Besançon : Algèbre et Théorie des Nombres, Publications mathématiques de Besançon, 2016. 〈hal-01295254〉

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