Definability via the tilting correspondence
arXiv:2605.23466
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.
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