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Character variety and étale slice of the representation space of a group. (Variété des caractères et slice étale de l’espace des représentations d’un groupe.) (French) Zbl 1056.20032

Summary: Let \(\Gamma\) be a finitely presented group such that \(\Gamma/\Gamma'\) is isomorphic to \(\mathbb{Z}\) and let \(G\) be an algebraic complex connected reductive group. We use the notion of étale slice to describe the local structure of the character variety \(X(\Gamma,G)\) near a class of Abelian representations. Furthermore, we construct an explicit étale slice and prove that the Zariski tangent space to the character variety may not be isomorphic to the first cohomology group.

MSC:

20G05 Representation theory for linear algebraic groups
14L30 Group actions on varieties or schemes (quotients)
20G10 Cohomology theory for linear algebraic groups
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References:

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