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arXiv · 2309.06396

On extensions of number fields with given quadratic algebras and cohomology

Oussama Hamza
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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.

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Oussama Hamza. 2023-09-12. On extensions of number fields with given quadratic algebras and cohomology. https://arxiv.org/abs/2309.06396

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