Forms of almost homogeneous varieties over perfect fields
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866914772177387520 |
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| author | Moser-Jauslin, Lucy Terpereau, Ronan |
| author_facet | Moser-Jauslin, Lucy Terpereau, Ronan |
| contents | We study the k-forms of almost homogeneous varieties over perfect base fields k. First, we discuss criteria for the existence of k-forms in the homogeneous case. Then, we extend the Luna-Vust theory from algebraically closed fields to perfect fields to determine when a given k-form of the open orbit of an almost homogeneous variety extends to a k-form of the entire variety. Finally, in the last section, we apply these results to determine the real forms of complex almost homogeneous SL(2)-threefolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_05197 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Forms of almost homogeneous varieties over perfect fields Moser-Jauslin, Lucy Terpereau, Ronan Algebraic Geometry 14M17, 20G15, 14M27, 14P99 We study the k-forms of almost homogeneous varieties over perfect base fields k. First, we discuss criteria for the existence of k-forms in the homogeneous case. Then, we extend the Luna-Vust theory from algebraically closed fields to perfect fields to determine when a given k-form of the open orbit of an almost homogeneous variety extends to a k-form of the entire variety. Finally, in the last section, we apply these results to determine the real forms of complex almost homogeneous SL(2)-threefolds. |
| title | Forms of almost homogeneous varieties over perfect fields |
| topic | Algebraic Geometry 14M17, 20G15, 14M27, 14P99 |
| url | https://arxiv.org/abs/2008.05197 |