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
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     title = {Lubin{\textquoteright}s conjecture for full $p$-adic dynamical systems},
     journal = {Publications math\'ematiques de Besan\c{c}on. Alg\`ebre et th\'eorie des nombres},
     pages = {19--24},
     publisher = {Presses universitaires de Franche-Comt\'e},
     year = {2016},
     doi = {10.5802/pmb.o-2},
     zbl = {1429.11208},
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Laurent Berger. 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. https://pmb.centre-mersenne.org/articles/10.5802/pmb.o-2/

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