Quotients of absolute Galois groups which determine the entire Galois cohomology

Chebolu, Sunil K.; Efrat, Ido; Mináč, Ján

doi:10.1007/s00208-011-0635-6

Cited by 58 publications

(48 citation statements)

References 34 publications

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“…These calculations have seen a recent resurgence of interest in [5,10,12,35], especially in connection with the Merkurjev-Suslin Theorem [22] and the Bloch-Kato conjecture, which is now a theorem of Voevodsky-Rost et al [31,37,39]. The MerkurjevSuslin Theorem is sufficient for our considerations here.…”

Section: Galois Cohomologymentioning

confidence: 98%

The Galois action on geometric lattices and the mod- $$\ell $$ ℓ I/OM

Topaz

2018

Invent. math.

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Section: Galois Cohomologymentioning

confidence: 98%

The Galois action on geometric lattices and the mod- $$\ell $$ ℓ I/OM

Topaz

2018

Invent. math.

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“…Remark 7.4. As noted in [CEM,EM2], one can use [CEM,Proposition 9.1] (or [EM2, Corollary 6.3]) to show that various pro-2-groups do not occur as G F (2) for some field F of characteristic = 2. For the convenience of the reader, we recall this result for pro-2-groups as below.…”

Section: Groups Without the Triple Vanishing Propertymentioning

confidence: 99%

Triple Massey products and Galois theory

Mináč¹,

Tân²

2016

J. Eur. Math. Soc.

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We show that any triple Massey product with respect to prime 2 contains 0 whenever it is defined over any field. This extends the theorem of M. J. Hopkins and K. G. Wickelgren, from global fields to any fields. This is the first time when the vanishing of any n-Massey product for some prime p has been established for all fields. This leads to a strong restriction on the shape of relations in the maximal pro-2-quotients of absolute Galois groups, which was out of reach until now. We also develop an extension of Serre's transgression method to detect triple commutators in relations of pro-p-groups, where we do not require that all cup products vanish. We prove that all n-Massey products, n ≥ 3, vanish for general Demushkin groups. We formulate and provide evidence for two conjectures related to the structure of absolute Galois groups of fields. In each case when these conjectures can be verified, they have some interesting concrete Galois theoretic consequences. They are also related to the Bloch-Kato conjecture.

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“…The essential calculations concerning commutators and cup products were first carried out by Labute [Lab67] (see also the exposition in [NSW08] §3.9). These calculations have seen a recent resurgence in [CEM12], [EM11], [EM15], [Top15], especially in connection with the Merkurjev-Suslin Theorem [MS82] and the recent proof of the Bloch-Kato conjecture due to Voevodsky-Rost et al [Voe11], [Ros98], [Wei09]. Nevertheless, the Merkurjev-Suslin Theorem [MS82] suffices for the considerations in this section, and we summarize the appropriate cohomological and group-theoretical calculations below.…”

Section: The Zassenhauss Filtration and Galois Cohomologymentioning

confidence: 99%

Reconstructing function fields from rational quotients of mod- $$\ell $$ ℓ Galois groups

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2015

Math. Ann.

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In this paper, we develop the main step in the global theory for the mod-ℓ analogue of Bogomolov's program in birational anabelian geometry for higher-dimensional function fields over algebraically closed fields. More precisely, we show how to reconstruct a function field K of transcendence degree ≥ 5 over an algebraically closed field, up-to inseparable extensions, from the mod-ℓ abelian-by-central Galois group of K endowed with the collection of mod-ℓ rational quotients.

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Quotients of absolute Galois groups which determine the entire Galois cohomology

Abstract: Abstract. For a prime power q = p d and a field F containing a root of unity of order q we show that the Galois cohomology ring H *

Cited by 58 publications

References 34 publications

The Galois action on geometric lattices and the mod- $$\ell $$ ℓ I/OM

The Galois action on geometric lattices and the mod- $$\ell $$ ℓ I/OM

Triple Massey products and Galois theory

Reconstructing function fields from rational quotients of mod- $$\ell $$ ℓ Galois groups

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