Decidability via the tilting correspondence
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911914597023744 |
|---|---|
| author | Kartas, Konstantinos |
| author_facet | Kartas, Konstantinos |
| contents | We prove a relative decidability result for perfectoid fields. This applies to show that the fields $\mathbb{Q}_p(p^{1/p^{\infty}})$ and $\mathbb{Q}_p(ζ_{p^{\infty}})$ are (existentially) decidable relative to the perfect hull of $ \mathbb{F}_p(\!(t)\!)$ and $\mathbb{Q}_p^{ab}$ is (existentially) decidable relative to the perfect hull of $\overline{ \mathbb{F}}_p(\!(t)\!)$. We also prove some unconditional decidability results in mixed characteristic via reduction to characteristic $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_04424 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Decidability via the tilting correspondence Kartas, Konstantinos Logic Number Theory We prove a relative decidability result for perfectoid fields. This applies to show that the fields $\mathbb{Q}_p(p^{1/p^{\infty}})$ and $\mathbb{Q}_p(ζ_{p^{\infty}})$ are (existentially) decidable relative to the perfect hull of $ \mathbb{F}_p(\!(t)\!)$ and $\mathbb{Q}_p^{ab}$ is (existentially) decidable relative to the perfect hull of $\overline{ \mathbb{F}}_p(\!(t)\!)$. We also prove some unconditional decidability results in mixed characteristic via reduction to characteristic $p$. |
| title | Decidability via the tilting correspondence |
| topic | Logic Number Theory |
| url | https://arxiv.org/abs/2001.04424 |