Four-fold Massey products in Galois cohomology
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Bibliographic record
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.
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