Existence of global Néron models beyond semi-abelian varieties
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866908284503457792 |
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| author | Overkamp, Otto Suzuki, Takashi |
| author_facet | Overkamp, Otto Suzuki, Takashi |
| contents | We first prove Bosch-Lütkebohmert-Raynaud's conjectures on existence of global Néron models of not necessarily semi-abelian algebraic groups in the perfect residue fields case. We then give a counterexample to the existence in the imperfect residue fields case. Finally, as a complement to the conjectures, we classify unirational wound unipotent groups "up to relative perfection", again in the perfect residue fields case. The key ingredient for all these is the duality for relatively perfect unipotent groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_14567 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Existence of global Néron models beyond semi-abelian varieties Overkamp, Otto Suzuki, Takashi Number Theory Algebraic Geometry 14L15 (Primary) 14G17, 14F30, 11G10, 14K15 (Secondary) We first prove Bosch-Lütkebohmert-Raynaud's conjectures on existence of global Néron models of not necessarily semi-abelian algebraic groups in the perfect residue fields case. We then give a counterexample to the existence in the imperfect residue fields case. Finally, as a complement to the conjectures, we classify unirational wound unipotent groups "up to relative perfection", again in the perfect residue fields case. The key ingredient for all these is the duality for relatively perfect unipotent groups. |
| title | Existence of global Néron models beyond semi-abelian varieties |
| topic | Number Theory Algebraic Geometry 14L15 (Primary) 14G17, 14F30, 11G10, 14K15 (Secondary) |
| url | https://arxiv.org/abs/2310.14567 |