Four-fold Massey products in Galois cohomology
Number Theory
2019-02-20 v4 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1610.05748,
title = {Four-fold Massey products in Galois cohomology},
author = {Pierre Guillot and Jan Minac and Adam Topaz and Olivier Wittenberg},
journal= {arXiv preprint arXiv:1610.05748},
year = {2019}
}
Comments
Final version: several corrections made throughout the paper; some sections reorganized; will appear in Compositio Mathematica