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Four-fold Massey products in Galois cohomology

Published online by Cambridge University Press:  17 August 2018

Pierre Guillot
Affiliation:
Université de Strasbourg & CNRS, Institut de Recherche Mathématique Avancée, UMR 7501, F-67000 Strasbourg, France email guillot@math.unistra.fr
Ján Mináč
Affiliation:
Department of Mathematics, Western University, London, Ontario, N6A 5B7, Canada email minac@uwo.ca
Adam Topaz
Affiliation:
Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK email topaz@maths.ox.ac.uk

Abstract

In this paper, we develop a new necessary and sufficient condition for the vanishing of $4$-Massey products of elements in the modulo-$2$ Galois cohomology of a field. This new description allows us to define a splitting variety for $4$-Massey products, which is shown in the appendix to satisfy a local-to-global principle over number fields. As a consequence, we prove that, for a number field, all such $4$-Massey products vanish whenever they are defined. This provides new explicit restrictions on the structure of absolute Galois groups of number fields.

Type
Research Article
Copyright
© The Authors 2018 

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