The Kummerian property and maximal pro-\(p\) Galois groups

DOI10.1016/j.jalgebra.2019.01.015zbMath1446.12005arXiv1707.07018OpenAlexW2736575451WikidataQ128452157 ScholiaQ128452157MaRDI QIDQ1730199

Claudio Quadrelli, Ido Efrat

Publication date: 11 March 2019

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.07018

zbMATH Keywords

Galois groupsGalois cohomologyKummer theorypro-\(p\) groupscyclotomic pro-\(p\) pairsmaximal pro-\(p\) Galois groups

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Galois cohomology (12G05) Limits, profinite groups (20E18) Field arithmetic (12E30)

Related Items

Oriented pro-\(\ell\) groups with the Bogomolov-Positselski property ⋮ Galois-theoretic features for 1-smooth pro-p groups ⋮ Enhanced Koszul properties in Galois cohomology ⋮ Right‐angled Artin pro‐p$p$ groups ⋮ Massey products in Galois cohomology and the elementary type conjecture ⋮ Frattini-resistant direct products of pro-\(p\) groups ⋮ Profinite groups with a cyclotomic \(p\)-orientation ⋮ Right-angled Artin groups and enhanced Koszul properties ⋮ Relations in the maximal pro-𝑝 quotients of absolute Galois groups ⋮ Two families of pro-\(p\) groups that are not absolute Galois groups ⋮ On pro-\(p\) groups with quadratic cohomology ⋮ Groups of \(p\)-absolute Galois type that are not absolute Galois groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Sylow subgroups of the absolute Galois group \(\mathrm{Gal}(\mathbb{Q})\)
• Triple Massey products and Galois theory
• Quotients of absolute Galois groups which determine the entire Galois cohomology
• A recursive description of the maximal pro-2 Galois group via Witt rings
• Homology, Massey products and maps between groups
• Small maximal pro-\(p\) Galois groups
• Demuškin fields with valuations
• Triple Massey products and absolute Galois groups
• Free-by-Demushkin pro-\(p\) groups.
• The Zassenhaus filtration, Massey products, and representations of profinite groups
• Algèbres de Lie et pro-p-groupes définis par une seule relation
• n-Nilpotent Obstructions to pi_1 Sections of P^1-{0,1,infty} and Massey Products
• Galois groups and cohomological functors
• Triple Massey products vanish over all fields
• On the descending central sequence of absolute Galois groups
• Bloch–Kato pro-p groups and locally powerful groups
• Massey products and ideal class groups
• Detecting fast solvability of equations via small powerful Galois groups
• Über Pro-p-Fundamentalgruppen markierter arithmetischer Kurven
• Galois Groups of Maximal p-Extensions
• Milnor invariants and Massey products for prime numbers
• Euklidische Körper und euklidische Hüllen von Körpern.
• On 3-Nilpotent Obstructions to π1 Sections for $$ \mathbb{P}^{1}_\mathbb{Q}$$−{0,1, $$\infty$$}
• Massey Higher Products
• Classification of Demushkin Groups
• Koszul property and Bogomolov's conjecture