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Four-fold Massey products in Galois cohomology

Part of: Operations and obstructions Homological methods (field theory)

Published online by Cambridge University Press:  17 August 2018

Pierre Guillot ,
Ján Mináč  and
Adam Topaz
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
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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.

Keywords

Massey productsGalois cohomologysplitting varietygroup cohomology

MSC classification

Primary: 55S30: Massey products 12G05: Galois cohomology

Information

Type
Research Article
Information
Compositio Mathematica , Volume 154 , Issue 9 , September 2018 , pp. 1921 - 1959
Copyright
© The Authors 2018 

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