Cohomology of uniserial p-adic space groups with cyclic point group

Oihana Garaialde Ocaña

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arXiv · 1706.06753

Cohomology of uniserial p-adic space groups with cyclic point group

Oihana Garaialde Ocaña

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Abstract

Let $p$ be a fixed prime number and let $R$ denote a uniserial $p$-adic space group of dimension $d_x=(p-1)p^{x-1}$ and with cyclic point group of order $p^x$. In this short note we prove that all the quotients of $R$ of size bigger than or equal to $p^{d_x+x}$ have isomorphic mod $p$ cohomology groups. In particular, we show that the cohomology groups of sufficiently large quotients of the unique maximal class pro-$p$ group are isomorphic as $\F_p$-modules.

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BibTeX RIS

Oihana Garaialde Ocaña. 2017-06-21. Cohomology of uniserial p-adic space groups with cyclic point group. https://arxiv.org/abs/1706.06753

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