Groups of automorphisms of local fields of period p^M and nilpotent class &lt;p

Abrashkin, Victor

doi:10.5802/aif.3093

Cited by 5 publications

(11 citation statements)

References 7 publications

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“…This fact and the remaining part of the proof appear as just a special case of the proof of Proposition 3.5 in [6].…”

Section: The Groupmentioning

confidence: 84%

“…Our exposition is not very far from Section 4 of [6], but we do not discuss the structure of ramification filtration, simplify constructions and correct some inexactitudes. Let R be Fontaine's ring.…”

Section: Application To the Mixed Characteristic Casementioning

confidence: 99%

“…(Here Γ (v) <p are the images of the ramification subgroups Γ (v) in Γ and all L (v) are ideals in L.) In the second part [7] of this paper we describe the ramification filtration L (v) , v 0, and find an explicit form of the Demushkin relation in terms related to this filtration. Note that a similar technique ( [6] and papers in progress) can be used to treat not only the similar quotients Γ <p (M ) of Γ of period p M but also the case of higher local fields K.…”

Section: Introductionmentioning

confidence: 99%

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Groups of automorphisms of local fields of period p and nilpotent class < p, I

Abrashkin

2017

Int. J. Math.

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. GROUPS OF AUTOMORPHISMS OF LOCAL FIELDS OF PERIOD p AND NILPOTENT CLASS < p, IVICTOR ABRASHKIN Abstract. Suppose K is a finite field extension of Q p containing a primitive p-th root of unity. Let K

2. Let K be a complete discrete valuation field with finite residue field k F p N 0 , N 0 ∈ N. Let K sep be a separable closure of K and Γ = Gal(K sep /K).A profinite group structure of Γ is well-known, [9]. Most significant information about this structure comes from the maximal p-quotient Γ(p) of Γ, [10,13,14]. As a matter of fact, the structure of Γ(p) is not too complicated: its (topological) module of generators equals K * /K * p and if K has no non-trivial p-th roots of unity (e.g. if charK = p) then Γ(p) is pro-finite free; otherwise, Γ(p) has finitely many generators and only one (the Demushkin) relation of a very special form. In [1, 2, 3] the author introduced new techniques (nilpotent ArtinSchreier theory) which allowed us to study p-extensions of characteristic p with Galois groups of nilpotent class < p. Such groups come from Lie algebras via classical equivalence L → G(L) of the categories of Lie

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“…This fact and the remaining part of the proof appear as just a special case of the proof of Proposition 3.5 in [6].…”

Section: The Groupmentioning

confidence: 84%

Section: Application To the Mixed Characteristic Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Groups of automorphisms of local fields of period p and nilpotent class < p, I

Abrashkin

2017

Int. J. Math.

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“…It was based on the combination of new techniques: nilpotent version of the Artin-Schreier theory developed by the author, and the Fontaine-Wintenberger theory of the field-of-norms functor. In the case of 1-dimensional local fields our method has been already applied in [6,7,8] to the study of the group Γ(p) modulo C p (Γ) together with the induced ramification filtration in terms of generators and relations.…”

Section: Introductionmentioning

confidence: 99%

Galois groups of p-extensions of higher local fields

Abrashkin

2020

Preprint

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“…Remark. The numbers v[s], 2 s < p, were found in [5] in a more general context of p-extensions with Galois groups of nilpotent class < p and period p M , M ∈ N, but the proof contains a gap. In Section 4 we gave a corrected version in the case M = 1; the same procedure can be applied in the case of arbitrary M .…”

Section: Introductionmentioning

confidence: 99%

Groups of automorphisms of local fields of period p and nilpotent class < p, II

Abrashkin

2017

Int. J. Math.

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Suppose [Formula: see text] is a finite field extension of [Formula: see text] containing a primitive [Formula: see text]th root of unity. Let [Formula: see text] be the maximal quotient of period [Formula: see text] and nilpotent class [Formula: see text] of the Galois group of a maximal [Formula: see text]-extension of [Formula: see text]. We describe the ramification filtration [Formula: see text] and relate it to an explicit form of the Demushkin relation for [Formula: see text]. The results are given in terms of Lie algebras attached to the appropriate [Formula: see text]-groups by the classical equivalence of the categories of [Formula: see text]-groups and Lie algebras of nilpotent class [Formula: see text].

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Groups of automorphisms of local fields of period p^M and nilpotent class <p

Abstract: Cet article est mis à disposition selon les termes de la licence CREATIVE COMMONS ATTRIBUTION-PAS DE MODIFICATION 3.

Cited by 5 publications

References 7 publications

Groups of automorphisms of local fields of period p and nilpotent class < p, I

Groups of automorphisms of local fields of period p and nilpotent class < p, I

Galois groups of p-extensions of higher local fields

Groups of automorphisms of local fields of period p and nilpotent class < p, II

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