Triple Massey products and absolute Galois groups

2014/12/23 by Ido Efrat, Efrat, Ido, Eliyahu Matzri +1 · 2 citations
Mathematics · #12E30 #12G05 #16K50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1412.7265

openalex publication_date 2014/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be a prime number, F a field containing a root of unity of order p, and G_F the absolute Galois group. Extending results of Hopkins, Wickelgren, Minac and Tan, we prove that the triple Massey product H¹(G_F)³→ H²(G_F) contains 0 whenever it is nonempty. This gives a new restriction on the possible profinite group structure of G_F.

Cited by

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

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