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), pp. 19-24.

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.

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.

Reçu le : 2016-03-29
Publié le : 2016-12-13
DOI : https://doi.org/10.5802/pmb.o-2
Classification : 11S82,  11S15,  11S20,  11S31,  13F25,  13F35,  14F30
Mots clés: p-adic dynamical system, Lubin-Tate formal group, p-adic Hodge theory
@article{PMB_2016____19_0,
     author = {Laurent Berger},
     title = {Lubin's conjecture for full $p$-adic dynamical systems},
     journal = {Publications Math\'ematiques de Besan\c con},
     pages = {19--24},
     publisher = {Presses universitaires de Franche-Comt\'e},
     year = {2016},
     doi = {10.5802/pmb.o-2},
     zbl = {1429.11208},
     language = {en},
     url = {pmb.centre-mersenne.org/item/PMB_2016____19_0/}
}
Laurent Berger. Lubin’s conjecture for full $p$-adic dynamical systems. Publications Mathématiques de Besançon (2016), pp. 19-24. doi : 10.5802/pmb.o-2. https://pmb.centre-mersenne.org/item/PMB_2016____19_0/

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