3-fold Massey products in Galois cohomology -The non-prime case

Ido Efrat

doi:10.48550/arXiv.2010.08970

3-fold Massey products in Galois cohomology -The non-prime case

Ido Efrat

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Working paper › Preprint

Abstract

For m≥2, let F be a field of characteristic prime to m and containing the roots of unity of order m, and let G_F be its absolute Galois group. We show that the 3-fold Massey products ⟨χ₁,χ₂,χ₃⟩, with χ₁,χ₂,χ₃∈H¹(G_F,Z/m) and χ₁,χ₃ Z/m-linearly independent, are non-essential. This was earlier proved for m prime. Our proof is based on the study of unitriangular representations of G_F.

Original language	English
DOIs	https://doi.org/10.48550/arXiv.2010.08970
State	Published - 18 Oct 2020

Keywords

12E30
12G05
16K50
Mathematics - Number Theory

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10.48550/arXiv.2010.08970

http://adsabs.harvard.edu/abs/2020arXiv201008970E

Cite this

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abstract = "For m≥2, let F be a field of characteristic prime to m and containing the roots of unity of order m, and let GF be its absolute Galois group. We show that the 3-fold Massey products ⟨χ1,χ2,χ3⟩, with χ1,χ2,χ3∈H1(GF,Z/m) and χ1,χ3 Z/m-linearly independent, are non-essential. This was earlier proved for m prime. Our proof is based on the study of unitriangular representations of GF.",

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N2 - For m≥2, let F be a field of characteristic prime to m and containing the roots of unity of order m, and let GF be its absolute Galois group. We show that the 3-fold Massey products ⟨χ1,χ2,χ3⟩, with χ1,χ2,χ3∈H1(GF,Z/m) and χ1,χ3 Z/m-linearly independent, are non-essential. This was earlier proved for m prime. Our proof is based on the study of unitriangular representations of GF.

AB - For m≥2, let F be a field of characteristic prime to m and containing the roots of unity of order m, and let GF be its absolute Galois group. We show that the 3-fold Massey products ⟨χ1,χ2,χ3⟩, with χ1,χ2,χ3∈H1(GF,Z/m) and χ1,χ3 Z/m-linearly independent, are non-essential. This was earlier proved for m prime. Our proof is based on the study of unitriangular representations of GF.

KW - 12E30

KW - 12G05

KW - 16K50

KW - Mathematics - Number Theory

U2 - 10.48550/arXiv.2010.08970

DO - 10.48550/arXiv.2010.08970

M3 - Preprint

BT - 3-fold Massey products in Galois cohomology -The non-prime case

ER -

3-fold Massey products in Galois cohomology -The non-prime case

Abstract

Keywords

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Cite this