Chern classes of complex Galois representations
type: Item
instance of: scholarly article
title: Chern classes of complex Galois representations
zbMATH Open document ID: 0770.12006
DOI: 10.1007/BF00534129
published in: \(K\)-Theory
publication date: 1993-01-16T00:00:00Z
review text: Let \(F\) be a field with absolute Galois group \(G_ F\). \(F\) is called exceptional if \(\text{Gal}(F(\mu_{2^ \infty})/F)\) contains torsion. If \(\rho:G_ F\to GL_ r(\mathbb{C})\) is a finite dimensional, continuous representation and if \(c_ i(\rho)\in H^{2i}(G_ F;\mathbb{Z})\) is the \(i\)th Chern class of \(\rho\) then the author proves that \(c_ i(\rho)=0\) if \(i\geq 2\) and \(F\) is nonexceptional. In any case, \(2c_ i(\rho)=0\). The author relates this to generalizations of a conjecture of K. Kato and suggests a generalization of his result to smooth varieties and their arithmetic filtration.
Mathematics Subject Classification ID: 12G05
Mathematics Subject Classification ID: 20J06
Mathematics Subject Classification ID: 55R40
zbMATH DE Number: 93461
zbMATH Keywords: characteristic classes
zbMATH Keywords: multiplicative transfer
zbMATH Keywords: Galois cohomology
author: Bruno Kahn
reviewed by: Victor P. Snaith
MaRDI profile type: Publication
cites work: Characters and cohomology of finite groups
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cites work: Q3762417
cites work: An Algebraic Characterisation of Chern Classes of Finite Group Representations
cites work: Generic Galois extensions and problems in field theory
cites work: Cohomologie galoisienne. Cours au Collège de France, 1962--1963. 3ième éd.
full work available at URL: https://doi.org/10.1007/bf00534129
OpenAlex ID: W2076115166
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description: scientific article; zbMATH DE number 93461