The Zassenhaus filtration, Massey products, and representations of profinite groups

Efrat, Ido

doi:10.1016/j.aim.2014.07.006

Cited by 48 publications

(64 citation statements)

References 17 publications

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“…In Section 2 we will present another (short and direct) proof for a result, which was first proved by I. Efrat [9], that every free pro-p-group has the kernel n-unipotent property for all n (Theorem 2.6, part a). At the same time, we obtain analogous new results for other filtrations, such as the descending central series and the descending p-central series.…”

Section: Introductionmentioning

confidence: 96%

The kernel unipotent conjecture and the vanishing of Massey products for odd rigid fields

Mináč

Tân

2015

Advances in Mathematics

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A major difficult problem in Galois theory is the characterization of profinite groups which are realizable as absolute Galois groups of fields. Recently the Kernel n-Unipotent Conjecture and the Vanishing n-Massey Conjecture for n ≥ 3 were formulated. These conjectures evolved in the last forty years as a byproduct of the application of topological methods to Galois cohomology. We show that both of these conjectures are true for odd rigid fields. This is the first case of a significant family of fields where both of the conjectures are verified besides fields whose Galois groups of p-maximal extensions are free pro-p-groups. We also prove the Kernel Unipotent Conjecture for Demushkin groups of rank 2, and establish various filtration results for free pro-p-groups, provide examples of pro-p-groups which do not have the kernel n-unipotent property, compare various Zassenhaus filtrations with the descending p-central series and establish new type of automatic Galois realization.

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Section: Introductionmentioning

confidence: 96%

The kernel unipotent conjecture and the vanishing of Massey products for odd rigid fields

Mináč

Tân

2015

Advances in Mathematics

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“…This implies that its n-fold Massey products, with n ≥ 3, are non-essential in the de Rahm context (see also [Huy05,Ch. 3 [Gär15], and the first-named author [Efr14].…”

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confidence: 99%

Triple Massey products and absolute Galois groups

Efrat¹,

Matzri²

2017

J. Eur. Math. Soc.

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“…Moreover, part of the interest of this result lies in the fact that the proof is purely group-theoretical, and it does not rely on results form field theory, according to the group-theoretical approach to Galois theory, which consists in translating the arithmetic information in group-theoretical terms, forgetting the arithmetic background (as it is done with Bloch-Kato pro-p groups, see [12]), in order to get as much information as possible on the structure of Galois pro-p groups using tools from the theory of pro-p groups. Further, the proof makes use of the Zassenhaus filtration of pro-p groups, which is gaining increasing importance as tool for the study of Galois groups (see, e.g., [5] and [11]). …”

Section: Corollarymentioning

confidence: 99%

Finite quotients of Galois pro- $$p$$ p groups and rigid fields

Quadrelli

2015

Ann. Math. Québec

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For a prime number p, the author shows that if two certain canonical finite quotients of a finitely generated Bloch-Kato pro-p group G coincide, then G has a very simple structure, i.e., G is a p-adic analytic pro-p group (see Theorem 1). This result has a remarkable Galoistheoretic consequence: if the two corresponding canonical finite extensions of a field F-with F containing a primitive p-th root of unity-coincide, then F is p-rigid (see Corollary 1). The proof relies only on group-theoretic tools, and on certain properties of Bloch-Kato pro-p groups.Résumé Étant donné un nombre premier p, l'auteur montre que si G est un pro-p groupe de Bloch-Kato de type fini dont deux quotients finis canoniques coïncident, alors G admet une structure est très simple: c'est un pro-p groupe p-adique analytique (voir théorème 1). Ce résultat a une conséquence remarquable pour la théorie de Galois: si un corps F contient une racine primitive p-ième de l'unité et que ses deux extensions canoniques finies correspondantes coïncident, F est alors p-rigide (voir corollaire 1). La démonstration s'appuie sur des résultats de théorie des groupes et exploite certaines propriétés des pro-p groupes de Bloch-Kato.

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The Zassenhaus filtration, Massey products, and representations of profinite groups

Cited by 48 publications

References 17 publications

The kernel unipotent conjecture and the vanishing of Massey products for odd rigid fields

The kernel unipotent conjecture and the vanishing of Massey products for odd rigid fields

Triple Massey products and absolute Galois groups

Finite quotients of Galois pro- $$p$$ p groups and rigid fields

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