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<p>We introduce a criterion on the presentation of finitely presented pro-<i>p</i> 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&#xa0;<i>p</i>-rational fields with prescribed ramification and splitting.</p>

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On extensions of number fields with given quadratic algebras and cohomology

  • 期刊论文

  • 发表日期：

    2025年1月9日

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  • Oussama Hamza

摘要

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.