Hom schemes for algebraic groups
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917086903664640 |
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| author | Cotner, Sean |
| author_facet | Cotner, Sean |
| contents | In SGA3, Demazure and Grothendieck showed that if $G$ and $H$ are smooth affine group schemes over a scheme $S$ and $G$ is reductive, then the functor of $S$-homomorphism $G \to H$ is representable. In this paper we extend this result to cover cases in which $G$ is not reductive, with much simpler proofs. Our results apply in particular to parabolics over any base, and they are essentially optimal over a field. We also relate the closed orbits in Hom schemes to Serre's theory of complete reducibility, answer a question of Furter--Kraft, and provide many examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_16458 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hom schemes for algebraic groups Cotner, Sean Algebraic Geometry Number Theory 14L40, 20G15, 20G35 In SGA3, Demazure and Grothendieck showed that if $G$ and $H$ are smooth affine group schemes over a scheme $S$ and $G$ is reductive, then the functor of $S$-homomorphism $G \to H$ is representable. In this paper we extend this result to cover cases in which $G$ is not reductive, with much simpler proofs. Our results apply in particular to parabolics over any base, and they are essentially optimal over a field. We also relate the closed orbits in Hom schemes to Serre's theory of complete reducibility, answer a question of Furter--Kraft, and provide many examples. |
| title | Hom schemes for algebraic groups |
| topic | Algebraic Geometry Number Theory 14L40, 20G15, 20G35 |
| url | https://arxiv.org/abs/2309.16458 |