Infinitesimal rational actions
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917497317359616 |
|---|---|
| author | Gouthier, Bianca |
| author_facet | Gouthier, Bianca |
| contents | For any finite $k$-group scheme $G$ acting rationally on a $k$-variety, if the action is generically free then the dimension of $\mathrm{Lie} (G)$ is upper bounded by the dimension of the variety. We show that this is the only obstruction when $k$ is a perfect field of positive characteristic and $G$ is infinitesimal commutative trigonalizable. We also give necessary conditions to have faithful rational actions of infinitesimal commutative trigonalizable group schemes on varieties, and (different) sufficient conditions in the unipotent case over a perfect field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01765 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Infinitesimal rational actions Gouthier, Bianca Algebraic Geometry For any finite $k$-group scheme $G$ acting rationally on a $k$-variety, if the action is generically free then the dimension of $\mathrm{Lie} (G)$ is upper bounded by the dimension of the variety. We show that this is the only obstruction when $k$ is a perfect field of positive characteristic and $G$ is infinitesimal commutative trigonalizable. We also give necessary conditions to have faithful rational actions of infinitesimal commutative trigonalizable group schemes on varieties, and (different) sufficient conditions in the unipotent case over a perfect field. |
| title | Infinitesimal rational actions |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2312.01765 |