The Chern classes modulo \(p\) of a regular representation
type: Item
instance of: scholarly article
title: The Chern classes modulo \(p\) of a regular representation
zbMATH Open document ID: 0954.20028
published in: Documenta Mathematica
publication date: 1999-06-06T00:00:00Z
full work available at URL: https://eudml.org/doc/228975
full work available at URL: 06.html
review text: Let \(r_G\) be a complex regular representation of a finite group \(G\) and \(c_i(r_G)\) the mod \(p\) Chern class [\textit{M. F. Atiyah}, Publ. Math., Inst. Hautes Etud. Sci. 9, 247-288 (1961; Zbl 0107.02303)] of the representation \(r_G\). \textit{B. B. Venkov} [Dokl. Akad. Nauk SSSR 137, 1274-1277 (1961; Zbl 0116.25903)] announced that \(c_i(r_G)=0\) for \(i<p^n-p^{n-1}\), where \(p^n\) is the highest power of a prime \(p\) dividing the order \(|G|\). The author makes use of his methods presented earlier [J. Algebra 144, No. 1, 214-247 (1991; Zbl 0777.20019)] to show that this assertion is valid for any finite group \(G\).
Mathematics Subject Classification ID: 20J06
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 1295629
zbMATH Keywords: finite groups
zbMATH Keywords: Chern classes
zbMATH Keywords: regular representations
author: Bruno Kahn
reviewed by: Marek Golasiński
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1295629