The tilting equivalence as a bi-interpretation

TL;DR

This paper provides a model theoretic interpretation of the equivalence between mixed characteristic perfectoid spaces and their tilts, offering new insights into their structural relationship.

Contribution

It introduces a novel model theoretic framework to understand the tilting equivalence in perfectoid spaces.

Findings

Establishes a formal bi-interpretation of the tilting equivalence.

Bridges model theory and perfectoid space theory.

Provides a new perspective on the structural properties of perfectoid spaces.

Abstract

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