On extensions of number fields with given quadratic algebras and cohomology: On extensions of number fields with given quadratic algebras...: O. Hamza.

We introduce a criterion on the presentation of finitely presented pro-p groups which allows us to compute their cohomology groups and infer non-analytic quotients, with 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. [ABSTRACT FROM AUTHOR]