On extensions of number fields with given quadratic algebras and cohomology

2023/09/12 by Oussama Hamza, Hamza, Oussama · 2 citations
Computer Science · Mathematics · #12G10 #17A45 #20F05 #20F40 #20J05 #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2309.06396

openalex publication_date 2023/09/12 · openalex created_date 2023/09/14 · openalex updated_date 2026/07/28

Abstract

We introduce a criterion on the presentation of finitely presented pro-p groups which allows us to compute their cohomology groups and infer quotients of mild groups of cohomological dimension strictly larger than two, from (non-free) mild groups. We interpret these groups as Galois groups over p-rational fields with prescribed ramification and splitting.

Cited by

• Maximal 2-extensions of Pythagorean fields and Right Angled Artin Groups
• Massey products and unipotent extensions with restricted ramification

Related

• Mild pro-p-groups and p-extensions of imaginary quadratic fields with non-trivial p-class group
• Combinatorial Techniques in the Galois Theory of p-Extensions
• The first two cohomology groups of some Galois groups
• The Galois group of a Special Group
• Unramified extensions over low degree number fields