Integral cohomology of classical groups over a finite field
type: Item
instance of: scholarly article
title: Integral cohomology of classical groups over a finite field
zbMATH Open document ID: 0840.20037
DOI: 10.1016/0022-4049(93)90161-L
author: Denis Jeandupeux
published in: Journal of Pure and Applied Algebra
publication date: 1993-05-16T00:00:00Z
review text: Let \(G\) be one of the groups \(GL_n\), \(SL_n\), \(U_n\), \(SU_n\) or \(Sp\) over a finite field of characteristic \(p\). The author calculates the order of the integral Chern classes, obtained by Brauer lifting. The proof uses a description of the \(\text{mod }l\) cohomology of \(G\), for each prime \(l\) distinct from \(p\). For \(GL_n\) this description is done by \textit{D. Quillen} [Ann. Math., II. Ser. 96, 552-586 (1972; Zbl 0249.18022)]\ and for \(U_n\) and \(Sp\) by \textit{Z. Fiedorowicz} and \textit{S. Priddy} [Homology of classical groups over finite fields and their associated infinite loop spaces (Lect. Notes Math. 674, 1978; Zbl 0403.55010)]. The author computes this cohomology for the special groups \(SL_n\) and \(SU_n\).
Mathematics Subject Classification ID: 20G10
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 166162
zbMATH Keywords: classical groups
zbMATH Keywords: finite field
zbMATH Keywords: integral Chern classes
zbMATH Keywords: Brauer lifting
zbMATH Keywords: cohomology
MaRDI profile type: Publication
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full work available at URL: 0022-4049(93)90161-l
OpenAlex ID: W2032213624
description: scientific article; zbMATH DE number 166162