Appears in collection : Model theory of valued fields / Théorie des modèles des corps valués
Given a perfectoid field, we find an elementary extension and an especially nice valuation on it whose residue field is an elementary extension of the tilt. This specializes to the almost purity theorem over perfectoid valuation rings and Fontaine-Wintenberger. Along the way, we prove an Ax-Kochen/Ershov principle for certain deeply ramified fields, which also uncovers some new model-theoretic phenomena in positive characteristic. Notably, we get that the perfect hull of $\mathbb{F}_p(t)^h$ is an elementary substructure of the perfect hull of $\mathbb{F}_p((t))$. Joint work with Franziska Jahnke.
By Vincent Neiger
By Vincent Neiger
By François-Xavier Vialard
By Jean Feydy
By Thibaut Le Gouic
By Elsa Cazelles
By Olga Mula Hernandez
