On geometrically $C_1$ fields
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916338839060480 |
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| author | Kartas, Konstantinos |
| author_facet | Kartas, Konstantinos |
| contents | A field $k$ is called geometrically $C_1$ if every smooth projective separably rationally connected $k$-variety has a $k$-rational point. Given a henselian valued field of equal characteristic $0$ with divisible value group, we show that the property of being geometrically $C_1$ lifts from the residue field to the valued field. We also prove that algebraically maximal valued fields with divisible value group and finite residue field are geometrically $C_1$. In particular, any maximal totally ramified extension of a local field is geometrically $C_1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19986 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On geometrically $C_1$ fields Kartas, Konstantinos Algebraic Geometry Logic Number Theory A field $k$ is called geometrically $C_1$ if every smooth projective separably rationally connected $k$-variety has a $k$-rational point. Given a henselian valued field of equal characteristic $0$ with divisible value group, we show that the property of being geometrically $C_1$ lifts from the residue field to the valued field. We also prove that algebraically maximal valued fields with divisible value group and finite residue field are geometrically $C_1$. In particular, any maximal totally ramified extension of a local field is geometrically $C_1$. |
| title | On geometrically $C_1$ fields |
| topic | Algebraic Geometry Logic Number Theory |
| url | https://arxiv.org/abs/2407.19986 |