Publications Mathématiques de Besançon
Algèbre et Théorie des Nombres
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Laurent Berger
Lubin’s conjecture for full $p$-adic dynamical systems
(La conjecture de Lubin pour les systèmes dynamiques $p$-adiques pleins)
Publications mathématiques de Besançon (2016), p. 19-24
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Class. Math.: 11S82, 11S15, 11S20, 11S31, 13F25, 13F35, 14F30
Keywords: $p$-adic dynamical system, Lubin-Tate formal group, $p$-adic Hodge theory

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 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.

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