7 papers
Tame Galois Groups, Linking Numbers and Mildness
Julian Feuerpfeil, Oussama Hamza, Donghyeok Lim
Let be an odd prime and let be a set of tame primes. We denote by the Galois group of the maximal pro- extension of unramified outside . We prove t…
Filtrations and cohomology on graph products
Oussama Hamza
Let be a prime. We resolve a question posed by Mináč-Rogelstad-Tân. We relate the Zassenhaus and the lower central series of pro- groups under a torsion-freeness condition.…
Maximal -extensions of Pythagorean fields and Right Angled Artin Groups
Oussama Hamza, Christian Maire, Ján Mináč +1
In this paper, we describe minimal presentations of maximal pro- quotients of absolute Galois groups of formally real Pythagorean fields of finite type. For this purpose, we int…
Massey products and unipotent extensions with restricted ramification
Oussama Hamza, Donghyeok Lim, Christian Maire
We fix a prime p and construct new cases of pro-p extensions of number fields with restricted ramification and splitting, whose Galois groups decompose as coproducts of pro-p absol…
On extensions of number fields with given quadratic algebras and cohomology
Oussama Hamza
We introduce a criterion on the presentation of finitely presented pro- groups which allows us to compute their cohomology groups and infer quotients of mild groups of cohomolog…
Zassenhaus and lower central filtrations of pro- groups considered as modules
Oussama Hamza
The goal of this paper is to study Zassenhaus and lower central filtrations of finitely generated pro- groups in an isotypical context. We shall focus on the semisimple case. Pa…
A note on asymptotically good extensions in which infinitely many primes split completely
Oussama Hamza, Christian Maire
Let p be a prime number, and let K be a number field. For p=2, assume moreover K totally imaginary. In this note we prove the existence of asymptotically good extensions L{K of coh…