Four-fold Massey products in Galois cohomology

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...

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Bibliographic Details
Published in:Compositio mathematica 2018-09, Vol.154 (9), p.1921-1959
Main Authors: Guillot, Pierre, Mináč, Ján, Topaz, Adam
Format: Article
Language:English
Subjects:
Algebraic Geometry
Homology
Mathematics
Number Theory
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Summary: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.
ISSN:0010-437X
1570-5846
DOI:10.1112/S0010437X18007297