Appears in collection : Arithmetic of fields: model theory, valuations, and geometry / L'arithmétiques des corps : théories des modèles, valuations, et geometrie

We aim to identify a class of Banach rings for which a certain foundational result about perfectoid rings—true only in an “almost sense”—becomes genuinely true. To this end, we introduce the notion of tame Banach rings, extending the notion of a tame field, and prove that they satisfy the desired property for Galois covers of p-power degree. We also outline some ideas towards the case of general etale covers. Joint work with Franziska Jahnke.