Vanishing of certain cohomology sets for \(\text{SL}_n(R_{\mathcal M})\)
type: Item
instance of: scholarly article
title: Vanishing of certain cohomology sets for \(\text{SL}_n(R_{\mathcal M})\)
zbMATH Open document ID: 1003.20040
author: Nicholas Hine Gajcowski
published in: Proceedings of the Japan Academy. Series A
publication date: 2002-08-18T00:00:00Z
review text: Let \((R,{\mathcal M)}\) be a complete local ring with finite residue field of odd characteristic \(p\). Let the group \(\langle g\rangle\) of order two with generator \(g\) act on \(\text{SL}_n(R)\) by \(g(A)=(A^{-1})^t\). So the group of fixed points is \(\text{SO}_n(R)\). The author shows that \(H^1(\langle g\rangle,\text{SL}_n(R))\) vanishes. This is then used to compute the order of \(\text{SO}_2(\mathbb{Z}/p^m)\).
reviewed by: Wilberd van der Kallen
Mathematics Subject Classification ID: 20G10
Mathematics Subject Classification ID: 20G35
zbMATH DE Number: 1782972
zbMATH Keywords: cohomology sets
zbMATH Keywords: orthogonal groups
zbMATH Keywords: local rings
zbMATH Keywords: groups of fixed points
MaRDI profile type: Publication
full work available at URL: pjaa.77.157
OpenAlex ID: W2059497493
cites work: Q5563439
cites work: On certain cohomology sets attached to Riemann surfaces
cites work: On certain cohomology set for \(\Gamma_0(N)\).
cites work: Q4349107
cites work: Spiral waves for the 2D Riemann problem for a compressible fluid
DOI: 10.3792/PJAA.77.157
description: scientific article; zbMATH DE number 1782972