Relations in the maximal pro-$p$ quotients of absolute Galois groups

TL;DR

This paper explores the structure of maximal pro-$p$ Galois groups of fields containing a primitive $p$th root of unity, extending classical local field results using Galois cohomology and Massey products.

Contribution

It generalizes fundamental Galois theoretical constructions from local fields to broader fields, revealing new restrictions on Galois group structures.

Findings

Restrictions on Galois group structures derived from cohomological methods

Extension of Demushkin, Labute, and Serre's ideas beyond local fields

Use of Massey products to analyze Galois groups

Abstract

We observe that some basic but fundamental constructions in Galois theory can be used to obtain some interesting restrictions on the structure of Galois groups of maximal $p$-extensions of fields containing a primitive $p$th root of unity. This is an extension of some significant ideas of Demushkin, Labute and Serre from local fields to all fields containing a primitive $p$th root of unity. Our techniques use certain natural simple Galois extensions together with some considerations in Galois cohomology and Massey products.