| Résume | The almost purity theorem is a foundational result in perfectoid geometry which, as the name suggests, holds only in an “almost” sense. We aim to identify a class of Banach rings for which the theorem holds in a genuine (non-almost) form. To this end, we introduce the notion of a tame Banach ring, extending the notion of a tame field, and prove that these rings satisfy the desired property for Galois covers of p-power degree. We also outline some ideas towards the case of general étale covers. Joint work with Franziska Jahnke. |
