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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.18163 |
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| _version_ | 1866911074490515456 |
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| author | Ocaña, Oihana Garaialde González-Sánchez, Jon Guerrero-Sánchez, Lander |
| author_facet | Ocaña, Oihana Garaialde González-Sánchez, Jon Guerrero-Sánchez, Lander |
| contents | Let $p$ be an odd prime, and let $n\in \N$ be an integer. We show that the $n^{\text{th}}$ mod-$p$ cohomology of a solvable saturable pro-$p$ group is isomorphic to the $n^{\text{th}}$ mod-$p$ cohomology of its associated $\Z_p$-Lie algebra $\g$ as a $\F_p$-vector space. Addittonally, we obtain that the $n^{\text{th}}$ mod-$p$ cohomology of $\g$ and of $\g/p\g$ are isomorphic as $\F_p$-vector spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18163 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cohomology of solvable saturable pro-$p$ groups and Lie algebras Ocaña, Oihana Garaialde González-Sánchez, Jon Guerrero-Sánchez, Lander Algebraic Topology Group Theory Let $p$ be an odd prime, and let $n\in \N$ be an integer. We show that the $n^{\text{th}}$ mod-$p$ cohomology of a solvable saturable pro-$p$ group is isomorphic to the $n^{\text{th}}$ mod-$p$ cohomology of its associated $\Z_p$-Lie algebra $\g$ as a $\F_p$-vector space. Addittonally, we obtain that the $n^{\text{th}}$ mod-$p$ cohomology of $\g$ and of $\g/p\g$ are isomorphic as $\F_p$-vector spaces. |
| title | Cohomology of solvable saturable pro-$p$ groups and Lie algebras |
| topic | Algebraic Topology Group Theory |
| url | https://arxiv.org/abs/2507.18163 |