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Main Authors: Ocaña, Oihana Garaialde, González-Sánchez, Jon, Guerrero-Sánchez, Lander
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2507.18163
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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.
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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