# The Massey vanishing conjecture for number fields

## TL;DR

This paper proves the Massey vanishing conjecture for all number fields, confirming that certain higher-order Galois cohomology products always vanish in this setting.

## Contribution

It establishes the conjecture for number fields, advancing understanding of Galois cohomology and Massey products in algebraic number theory.

## Key findings

- Proves the Massey vanishing conjecture for number fields
- Confirms the vanishing of higher Massey products in this context
- Enhances knowledge of Galois cohomology structures

## Abstract

A conjecture of Min\'a\v{c} and T\^an predicts that for any n>2, any prime p and any field k, the Massey product of n Galois cohomology classes in H^1(k,Z/pZ) must vanish if it is defined. We establish this conjecture when k is a number field.