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arXiv · 1610.05748

Four-fold Massey products in Galois cohomology

Pierre Guillot·Jan Minac·Adam Topaz·Olivier Wittenberg
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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 mod-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.

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Pierre Guillot, Jan Minac, Adam Topaz, Olivier Wittenberg. 2016-10-18. Four-fold Massey products in Galois cohomology. https://doi.org/10.1112/s0010437x18007297

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