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

2018/08/06 by Minac, Jan, Rogelstad, Michael, Tan, Nguyen Duy
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1808.01705

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 pth 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 pth root of unity. Our techniques use certain natural simple Galois extensions together with some considerations in Galois cohomology and Massey products.

Related

• The Elementary Type Conjecture for Maximal Pro-p Galois groups
• Detecting pro-p-groups that are not absolute Galois groups, expanded version
• Combinatorial Techniques in the Galois Theory of p-Extensions
• Galois module structure of some elementary p-abelian extensions
• Demushkin groups and inverse Galois theory for pro-p-groups of finite rank and maximal p-extensions