Lubin’s conjecture for full p-adic dynamical systems
Publications mathématiques de Besançon. Algèbre et théorie des nombres (2016), pp. 19-24.

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 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.

Nous donnons une démonstration courte d’une conjecture de Lubin concernant certaines familles de séries formelles p-adiques qui commutent pour la composition. Nous montrons que si la famille est pleine (assez grosse), il existe un groupe formel de Lubin-Tate tel que toutes les séries de la famille sont des endomorphismes de ce groupe. La démonstration utilise la théorie de la ramification et un peu de théorie de Hodge p-adique.

Received:
Published online:
DOI: 10.5802/pmb.o-2
Classification: 11S82,  11S15,  11S20,  11S31,  13F25,  13F35,  14F30
Keywords: p-adic dynamical system, Lubin-Tate formal group, p-adic Hodge theory
Berger, Laurent 1

1 UMPA de l’ENS de Lyon, UMR 5669 du CNRS, IUF
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Berger, Laurent. Lubin’s conjecture for full $p$-adic dynamical systems. Publications mathématiques de Besançon. Algèbre et théorie des nombres (2016), pp. 19-24. doi : 10.5802/pmb.o-2. http://archive.numdam.org/articles/10.5802/pmb.o-2/

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