Four-fold Massey products in Galois cohomology

Pierre Guillot (1) , Ján Mináč (2) , Adam Topaz (3) , Olivier Wittenberg (4, 5)

1 IRMA - Institut de Recherche Mathématique Avancée
2 UWO - University of Western Ontario
3 MI - Mathematical Institute [Oxford]
4 CNRS - Centre National de la Recherche Scientifique
5 DMA - Département de Mathématiques et Applications - ENS Paris

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.

Domaines: Théorie des nombres [math.NT]; Géométrie algébrique [math.AG]

Pierre Guillot, Ján Mináč, Adam Topaz, Olivier Wittenberg. Four-fold Massey products in Galois cohomology. Compositio Mathematica, 2018, 154 (9), pp.1921-1959. ⟨10.1112/S0010437X18007297⟩. ⟨hal-02371601⟩