Abstract:We show that arithmetic definability of henselian valuations is preserved by the tilting correspondence. Moreover, we show that if a perfectoid valuation is arithmetically definable, then no parameters are needed. We also investigate whether these definitions can be chosen uniformly, and discuss the required quantifier complexity.
| Comments: | This work presents the results of the project "Arithmetic Definability of Henselian Valuations", one of the projects of the event "Women in Numbers Europe 5" which took place in Split, Croatia, in summer 2025 |
| Subjects: | Logic (math.LO); Number Theory (math.NT) |
| Cite as: | arXiv:2605.23466 [math.LO] |
| (or arXiv:2605.23466v1 [math.LO] for this version) | |
| https://doi.org/10.48550/arXiv.2605.23466 arXiv-issued DOI via DataCite (pending registration) |
From: Franziska Jahnke [view email]
[v1]
Fri, 22 May 2026 10:26:28 UTC (28 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。