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Decidability via the tilting correspondence

Konstantinos Kartas

Vol. 18 (2024), No. 2, 209–248
Abstract

We prove a relative decidability result for perfectoid fields. This applies to show that the fields p(p1p ) and p(ζp) are (existentially) decidable relative to the perfect hull of 𝔽p((t)) and pab is (existentially) decidable relative to the perfect hull of 𝔽¯p((t)). We also prove some unconditional decidability results in mixed characteristic via reduction to characteristic p.

Keywords
perfectoid fields, model theory, valued fields, decidability, tilting, tame fields
Mathematical Subject Classification 2010
Primary: 11U05
Secondary: 11U09
Milestones
Received: 14 February 2020
Revised: 16 December 2022
Accepted: 13 April 2023
Published: 6 February 2024
Authors
Konstantinos Kartas
Institut Mathématique de Jussieu
CNRS/IMJ-PRG
Paris
France

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