Elsevier

Advances in Mathematics

Volume 304, 2 January 2017, Pages 1021-1054
Advances in Mathematics

Construction of unipotent Galois extensions and Massey products

Dedicated to Alexander Merkurjev
https://doi.org/10.1016/j.aim.2016.09.014Get rights and content
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Abstract

For all primes p and for all fields, we find a sufficient and necessary condition of the existence of a unipotent Galois extension of degree p6. 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.

Keywords

Explicit Galois extensions
Massey products

Cited by (0)

JM is partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) grant R0370A01. NDT is partially supported by the National Foundation for Science and Technology Development (NAFOSTED) grant 101.04-2014.34.