Compactifications of a representation variety
| Autor: | Benjamin M. S. Martin |
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| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | jgth. 14:947-963 |
| ISSN: | 1435-4446 1433-5883 |
| Popis: | Let F be a finitely generated group and let G be a linear algebraic group over an algebraically closed field k. Let R(F, G) be the variety of representations of F in G. Given a finite set of generators Δ for F, we define a compactification RΔ(F, ) of R(F, G). The compactification depends on the choice of generators. If F′ is another finitely generated group with a finite set of generators Δ′ and ϕ : F′ → F is a homomorphism, then there is an induced morphism of varieties ϕ # : R(F, G) → R(F′, G). We prove that if ϕ(Δ′ ∪ {1}) ⊆ Δ ∪ {1}, then ϕ # extends to a morphism from RΔ(F, ) to RΔ′ (F′, ). We study the morphisms arising in this way from a group extension 1 → N → F → Q → 1. |
| Databáze: | OpenAIRE |
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