On geometrically $C_1$ fields
| Autor: | Kartas, Konstantinos |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $C_1$. Comment: 23 pages |
| Databáze: | arXiv |
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