Construction of unipotent Galois extensions and Massey products

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.

arXiv commentWe have improved our exposition following the referee's suggestions. The article will appear in the Advances in Mathematics