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Taming perfectoid fields

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Taming perfectoid fields

Tilting perfectoid fields, developed by Scholze, allows to transfer results between certain henselian fields of mixed characteristic and their positive characteristic counterparts and vice versa. We present a model-theoretic approach to tilting via ultraproducts, which allows to transfer many first-order properties between a perfectoid field and its tilt (and conversely). In particular, our method yields a simple proof of the Fontaine-Wintenberger Theorem which states that the absolute Galois group of a perfectoid field and its tilt are canonically isomorphic. A key ingredient in our approach is an Ax-Kochen/Ershov principle for perfectoid fields (and generalizations thereof).
This is joint work with Konstantinos Kartas.

- Séminaire Géométrie et théorie des modèles

Détails :

Orateur / Oratrice : Franziska Jahnke
Date : 25 novembre 2022
Horaire : 11h00 - 12h30
Lieu : IHP salle 01