The tilting equivalence as a bi-interpretation

Abstract

We propose a model theoretic interpretation of the theorems about the equivalence between mixed characteristic perfectoid spaces and their tilts.

We corrected the definition two issues in the previous version: - The definition of interpretation was weakened so that they do compose; - The proof of Fontaine-Wintenberger was rewritten to prove (and not use) that algebraic extensions of perfectoid fields are algebraic