Automorphismes des corps locaux de caractéristique p.

Wintenberger, Jean-Pierre

doi:10.5802/jtnb.455

Cited by 23 publications

(33 citation statements)

References 17 publications

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“…Laubie and Saïne [LS97,LS98] could later improve these results by applying Wintenberger's theory on fields of norms [Win04]. In [LMS02] the authors study Lubin's conjecture [Lub94], on the relation between wildly ramified power series and formal groups.…”

Section: Related Workmentioning

confidence: 99%

Characterization of 2-ramified power series

Nordqvist

2017

Journal of Number Theory

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Abstract. In this paper we study lower ramification numbers of power series tangent to the identity that are defined over fields of positive characteristics p. Let g be such a series, then g has a fixed point at the origin and the corresponding lower ramification numbers of g are then, up to a constant, the degree of the first non-linear term of p-power iterates of g. The result is a complete characterization of power series g having ramification numbers of the form 2(1 + p + · · · + p n ). Furthermore, in proving said characterization we explicitly compute the first significant terms of g at its pth iterate.

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Section: Related Workmentioning

confidence: 99%

Characterization of 2-ramified power series

Nordqvist

2017

Journal of Number Theory

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“…Note that, contrary to [2,6], we consider finite groups to be p-adic Lie groups. The equivalence of categories proved in [2,5,6] extends trivially to include the case of finite groups.…”

Section: Theorem 11 F Is An Equivalence Of Categoriesmentioning

confidence: 99%

“…Since H is an abelian p-adic Lie group, it follows from [2,5,6] that τ H is induced by an A-isomorphism…”

Section: Proof Of Proposition 32 Since G(c)h = G and C > φmentioning

confidence: 99%

Wintenberger’s functor for abelian extensions

Keating¹

2009

J. Théor. Nombres Bordeaux

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Let k be a finite field. Wintenberger used the field of norms to give an equivalence between a category whose objects are totally ramified abelian p-adic Lie extensions E/F , where F is a local field with residue field k, and a category whose objects are pairs (K, A), where K ∼ = k((T )) and A is an abelian p-adic Lie subgroup of Aut k (K). In this paper we extend this equivalence to allow Gal(E/F ) and A to be arbitrary abelian pro-p groups.

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“…1. Dans les « indications sur la démonstration » du théorème A données dans [8], il est montré qu'il suffit de le prouver dans le cas où G Z p ; et ce dernier cas est traité en détails dans [10]. Les équivalences (i) ⇔ (ii) et (iv) ⇔ (v) proviennent des propriétés classiques de la filtration du groupe des unités U .…”

Section: Ramification De Groupes De Séries Abéliensunclassified

Systèmes dynamiques et lois de groupe formel sur les corps finis

Laubie¹

2007

Journal of Number Theory

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Dans le même ordre d'idée que la « philosophie » de J. Lubin sur les systèmes dynamiques non archimé-diens, nous montrons comment toute famille finie de séries de F q [[X]] qui, pour la loi •, sont inversibles et commutent deux à deux, est reliée à une famille finie d'automorphismes d'une loi de groupe formel sur F q . Sous certaines hypothèses, ce groupe formel est une réduction sur F q d'un groupe formel de Lubin-Tate sur une extension finie de Q p . AbstractImitating the Lubin's philosophy on nonarchimedean dynamical systems, we prove that every finite family of inversibles series of F q [[X]] which commute for the law • is connected with a finite family of automorphisms of a formal group over F q . In some cases these formal groups are reduction on F q of Lubin-Tate formal groups over finite extensions of Q p .

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Automorphismes des corps locaux de caractéristique p.

Cited by 23 publications

References 17 publications

Characterization of 2-ramified power series

Characterization of 2-ramified power series

Wintenberger’s functor for abelian extensions

Systèmes dynamiques et lois de groupe formel sur les corps finis

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