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arXiv · 2605.23466

Definability via the tilting correspondence

Gessica Alecci·Ihsane Hadeg·Franziska Jahnke·Margarete Ketelsen·Isabella Negrini
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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.

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Gessica Alecci, Ihsane Hadeg, Franziska Jahnke, Margarete Ketelsen, Isabella Negrini. 2026-05-22. Definability via the tilting correspondence. https://arxiv.org/abs/2605.23466

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