Construction of unipotent Galois extensions and Massey products

TL;DR

This paper provides a necessary and sufficient condition for the existence of unipotent Galois extensions of degree p^6 over any field, offering a simple and general explicit construction that advances understanding in Galois theory and Massey products.

Contribution

It introduces a novel explicit construction of unipotent Galois extensions of degree p^6, resolving an open problem since 2003 and linking Galois theory with Massey products.

Findings

Characterizes when such Galois extensions exist for all primes p

Provides a simple, explicit construction method

Connects Galois extensions with Massey products in cohomology

Abstract

For all primes $p$ and all fields, we find a sufficient and necessary condition of the existence of a unipotent Galois extension of degree $p^6$. The main goal of this paper is to describe an explicit construction of such a Galois extension over fields admitting such a Galois extension. This construction is surprising in its simplicity and generality. The problem of finding such a construction has been left open since 2003. Recently a possible solution of this problem gained urgency because of an effort to extend new advances in Galois theory and its relations with Massey products in Galois cohomology.