Triple Massey products and absolute Galois groups

Efrat, Ido; Matzri, Eliyahu

doi:10.4171/jems/748

Cited by 47 publications

(55 citation statements)

References 10 publications

(14 reference statements)

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“…Nearly simultaneously with our arXiv posting of the first version of our paper, Efrat and Matzri posted [7] on arXiv. The paper [7] is a replacement of [14]. In [7], Efrat and Matzri also provide a cohomological approach to Theorem 4.10.…”

Section: Introductionmentioning

confidence: 99%

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Triple Massey products vanish over all fields

Mináč¹,

Tân

2016

J. London Math. Soc.

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Section: Introductionmentioning

confidence: 99%

“…The paper [7] is a replacement of [14]. In [7], Efrat and Matzri also provide a cohomological approach to Theorem 4.10. Their approach has a similar flavor to our proofs in this paper, but it is still different.…”

Section: Introductionmentioning

confidence: 99%

Triple Massey products vanish over all fields

Mináč¹,

Tân

2016

J. London Math. Soc.

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“…In the paper [38], this conjecture was proven for all the (one-dimensional) local and global fields. On the other hand, there is a series of recent papers [16,27,8,28] discussing and partially proving the conjecture that tuple Massey products of degree-one elements vanish in the cohomology algebra H * (G F , Z/l). The results above in this section and the discussion below show that the Koszulity conjecture implies vanishing of the tensor Massey products in H * (G F , Z/l), but may have no direct implications concerning the problem of vanishing of the tuple Massey products.…”

Section: Proof Notice That Any Morphism Of Augmented Dg-algebrasmentioning

confidence: 99%

“…The example of the relation (8) illustrates how the map (11) can fail to be an isomorphism in degree 4. One says that the system of nonhomogeneous quadratic relations R ⊂ N 2 F * is self-consistent if the algebra gr N A is defined by quadratic relations, or equivalently, if the map (11) is an isomorphism in all the degrees.…”

Section: Self-consistency Of Nonhomogeneous Quadratic Relationsmentioning

confidence: 99%

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Koszulity of cohomology = K(π,1)-ness + quasi-formality

Positselski

2017

Journal of Algebra

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Abstract. This paper is a greatly expanded version of [37, Section 9.11]. A series of definitions and results illustrating the thesis in the title (where quasi-formality means vanishing of a certain kind of Massey multiplications in the cohomology) is presented. In particular, we include a categorical interpretation of the "Koszulity implies K(π, 1)" claim, discuss the differences between two versions of Massey operations, and apply the derived nonhomogeneous Koszul duality theory in order to deduce the main theorem. In the end we demonstrate a counterexample providing a negative answer to a question of Hopkins and Wickelgren about formality of the cochain DG-algebras of absolute Galois groups, thus showing that quasi-formality cannot be strengthened to formality in the title assertion.

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Chasing Maximal Pro-p Galois Groups via 1-Cyclotomicity

Quadrelli

2024

Mediterr. J. Math.

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Let p be a prime. We prove that certain amalgamated free pro-p products of Demushkin groups with pro-p-cyclic amalgam cannot give rise to a 1-cyclotomic oriented pro-p group, and thus do not occur as maximal pro-p Galois groups of fields containing a root of 1 of order p. We show that other cohomological obstructions which are used to detect pro-p groups that are not maximal pro-p Galois groups—the quadraticity of $$\mathbb {Z}/p\mathbb {Z}$$ Z / p Z -cohomology and the vanishing of Massey products—fail with the above pro-p groups. Finally, we prove that the Minač–Tân pro-p group cannot give rise to a 1-cyclotomic oriented pro-p group, and we conjecture that every 1-cyclotomic oriented pro-p group satisfy the strong n-Massey vanishing property for $$n=3,4$$ n = 3 , 4 .

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Triple Massey products and absolute Galois groups

Cited by 47 publications

References 10 publications

Triple Massey products vanish over all fields

Triple Massey products vanish over all fields

Koszulity of cohomology = K(π,1)-ness + quasi-formality

Chasing Maximal Pro-p Galois Groups via 1-Cyclotomicity

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