Unexpected subgroup schemes of PGL_{2,k} in characteristic 2
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911797980692480 |
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| author | Gouthier, Bianca Tossici, Dajano |
| author_facet | Gouthier, Bianca Tossici, Dajano |
| contents | If the characteristic of a field $k$ is odd any infinitesimal group scheme of $PGL_{2,k}$ lifts to $SL_{2,k}$. In this paper, we prove that this is not true in characteristic $2$ and we give a complete description, up to isomorphism, of infinitesimal unipotent subgroup schemes of $PGL_{2,k}$. Also, the infinitesimal trigonalizable case is considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09469 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unexpected subgroup schemes of PGL_{2,k} in characteristic 2 Gouthier, Bianca Tossici, Dajano Algebraic Geometry Number Theory 14L15, 14L30 If the characteristic of a field $k$ is odd any infinitesimal group scheme of $PGL_{2,k}$ lifts to $SL_{2,k}$. In this paper, we prove that this is not true in characteristic $2$ and we give a complete description, up to isomorphism, of infinitesimal unipotent subgroup schemes of $PGL_{2,k}$. Also, the infinitesimal trigonalizable case is considered. |
| title | Unexpected subgroup schemes of PGL_{2,k} in characteristic 2 |
| topic | Algebraic Geometry Number Theory 14L15, 14L30 |
| url | https://arxiv.org/abs/2403.09469 |