On extensions of number fields with given quadratic algebras and cohomology
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912180523237376 |
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| author | Hamza, Oussama |
| author_facet | Hamza, Oussama |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_06396 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On extensions of number fields with given quadratic algebras and cohomology Hamza, Oussama Group Theory Number Theory 12G10, 20J05, 20F05, 20F40, 17A45 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. |
| title | On extensions of number fields with given quadratic algebras and cohomology |
| topic | Group Theory Number Theory 12G10, 20J05, 20F05, 20F40, 17A45 |
| url | https://arxiv.org/abs/2309.06396 |