Ramification of Some Automorphisms of Local Fields

Abstract

Let k be a perfect field of characteristic p and let # # Aut(k((t))). Define the ramification numbers of # by i m =v t (# p m (t)&t)&1. We give a characterization of the sequences (i m ) which are the sequences of ramification numbers of infinite order automorphisms of formal power series fields over finite fields. Then, given a perfect field k, we give sufficient conditions on (i m ) to be the sequence of ramification numbers of an autormorphism # # Aut k (k((t))) and we investigate these sequences (i m ) in the case where there exists _ # Aut k (k((t))) such that _#=#_ with _{#

Characterization of 2-ramified power series

“…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.…”

“…Lemma 1 is a restatement of the last statement of Corollary 1 in [LS98]. Our approach of calculating the pth iterate of g given in Proposition 1 is similar to methods used in [LRL16a,LRL16b].…”

On the numerology of ramification data for power series in characteristic p

“…3]. Note that the hypothesis in [4] that the Galois group of the maximal abelian pro-p extension of F is a free abelian pro-p group is automatically satisfied when char(F ) = p (see Theorem 8 and Remark 5 of [8]). Proof.…”

Automorphismes des corps locaux de caractéristique p.

“…Ce théorème a pour conséquences une généralisation du théorème de Hasse-Arf ( [23]), des propriétés de ramification d'éléments de A commutant ( [9], [10]). Il permet de déterminer presque complètement les suites d'entiers qui sont suite des nombres de ramification en numérotation supérieure d'uń elément de A ( [9], [10]).…”

“…Il permet de déterminer presque complètement les suites d'entiers qui sont suite des nombres de ramification en numérotation supérieure d'uń elément de A ( [9], [10]). …”