Cohomology of solvable saturable pro-p groups and Lie algebras

2025/07/24 by Ocaña, Oihana Garaialde, González-Sánchez, Jon, Guerrero-Sánchez, Lander
#Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2507.18163

Abstract

Let p be an odd prime, and let n∈ \N be an integer. We show that the n^th mod-p cohomology of a solvable saturable pro-p group is isomorphic to the n^th mod-p cohomology of its associated \Z_p-Lie algebra \g as a \F_p-vector space. Addittonally, we obtain that the n^th mod-p cohomology of \g and of \g/p\g are isomorphic as \F_p-vector spaces.

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