Triple Massey products in Galois cohomology

2014/11/15 by Eliyahu Matzri, Matzri, Eliyahu · 1 citation
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1411.4146

Abstract

Fix an arbitrary prime p. Let F be a field, containing a primitive p-th root of unity, with absolute Galois group G_F. The triple Massey product (in the mod-p Galois cohomology) is a partially defined, multi-valued function ⟨ ⋅,⋅,⋅ ⟩: H¹(G_F)³→ H²(G_F). In this work we prove a conjecture made in [11] stating that any defined triple Massey product contains zero. As a result the pro-p groups appearing in [11] are excluded from being absolute Galois groups of fields F as above.

Cited by

• The Elementary Type Conjecture for Maximal Pro-p Galois groups
• Counting Galois \mathbb U₄(\mathbb F_p)-extensions using Massey products

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