Oriented embedding functors of tori as homogeneous spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910809027772416 |
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| author | Gille, Philippe Lee, Ting-Yu |
| author_facet | Gille, Philippe Lee, Ting-Yu |
| contents | We provide a characterization of homogeneous spaces under a reductive group scheme such that the geometric stabilizers are maximal tori. The quasi-split case over a semilocal base is of special interest and permits to answer a question raised by Marc Levine on homogeneous SL$_n$-spaces. At the end, we provide an application to the local-global principles for embeddings of étale algebras with involution into central simple algebras with involution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_16475 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Oriented embedding functors of tori as homogeneous spaces Gille, Philippe Lee, Ting-Yu Algebraic Geometry We provide a characterization of homogeneous spaces under a reductive group scheme such that the geometric stabilizers are maximal tori. The quasi-split case over a semilocal base is of special interest and permits to answer a question raised by Marc Levine on homogeneous SL$_n$-spaces. At the end, we provide an application to the local-global principles for embeddings of étale algebras with involution into central simple algebras with involution. |
| title | Oriented embedding functors of tori as homogeneous spaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2307.16475 |