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Reductive subgroups of reductive groups in nonzero characteristic

✍ Scribed by Benjamin M.S. Martin

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 224 KB
Volume: 262
Category: Article
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(03)00189-3

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✦ Synopsis

Let G be a (possibly nonconnected) reductive linear algebraic group over an algebraically closed field k, and let N ∈ N. The group G acts on G N by simultaneous conjugation. Let H be a reductive subgroup of G. We prove that if k has nonzero characteristic then the natural map of quotient varieties H N /H → G N /G is a finite morphism. We use methods introduced by Vinberg, who proved the same result in characteristic zero. As an application, we show that if Γ is a finite group then the character variety C(Γ, G) of closed conjugacy classes of representations from Γ to G is finite.

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