Perfectoid $C_i$ transfer
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911378128764928 |
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| author | Kartas, Konstantinos |
| author_facet | Kartas, Konstantinos |
| contents | We prove a perfectoid analogue of the Ax-Kochen theorem on zeros of $p$-adic forms: Given $d\in \mathbb{N}$, there is a finite totally ramified extension $E/\mathbb{Q}_p$ such that every untilt of $\mathbb{F}_p(\!(t^{1/p^{\infty}})\!)$ containing $E$ is $C_2(d)$. We also prove a similar result for the existence of rational points in rationally connected varieties over perfectoid field extensions of $\mathbb{Q}_p^{ur}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14719 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Perfectoid $C_i$ transfer Kartas, Konstantinos Number Theory Algebraic Geometry Logic We prove a perfectoid analogue of the Ax-Kochen theorem on zeros of $p$-adic forms: Given $d\in \mathbb{N}$, there is a finite totally ramified extension $E/\mathbb{Q}_p$ such that every untilt of $\mathbb{F}_p(\!(t^{1/p^{\infty}})\!)$ containing $E$ is $C_2(d)$. We also prove a similar result for the existence of rational points in rationally connected varieties over perfectoid field extensions of $\mathbb{Q}_p^{ur}$. |
| title | Perfectoid $C_i$ transfer |
| topic | Number Theory Algebraic Geometry Logic |
| url | https://arxiv.org/abs/2504.14719 |