Morphisms of character varieties
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929361198776320 |
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| author | Cotner, Sean |
| author_facet | Cotner, Sean |
| contents | Let $k$ be a field, let $H \subset G$ be (possibly disconnected) reductive groups over $k$, and let $Γ$ be a finitely generated group. Vinberg and Martin have shown that the induced morphism of character varieties \[ \underline{\mathrm{Hom}}_{k\textrm{-gp}}(Γ, H)//H \to \underline{\mathrm{Hom}}_{k\textrm{-gp}}(Γ, G)//G \] is finite. In this note, we generalize this result (with a significantly different proof) by replacing $k$ with an arbitrary locally noetherian scheme, answering a question of Dat. Along the way, we use Bruhat-Tits theory to establish a few apparently new results about integral models of reductive groups over discrete valuation rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_10135 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Morphisms of character varieties Cotner, Sean Representation Theory Algebraic Geometry 20G35, 14L30, 14L15 Let $k$ be a field, let $H \subset G$ be (possibly disconnected) reductive groups over $k$, and let $Γ$ be a finitely generated group. Vinberg and Martin have shown that the induced morphism of character varieties \[ \underline{\mathrm{Hom}}_{k\textrm{-gp}}(Γ, H)//H \to \underline{\mathrm{Hom}}_{k\textrm{-gp}}(Γ, G)//G \] is finite. In this note, we generalize this result (with a significantly different proof) by replacing $k$ with an arbitrary locally noetherian scheme, answering a question of Dat. Along the way, we use Bruhat-Tits theory to establish a few apparently new results about integral models of reductive groups over discrete valuation rings. |
| title | Morphisms of character varieties |
| topic | Representation Theory Algebraic Geometry 20G35, 14L30, 14L15 |
| url | https://arxiv.org/abs/2304.10135 |