|Responsables :||Zoé Chatzidakis, Raf Cluckers|
|Email des responsables :||firstname.lastname@example.org|
Pour recevoir le programme par e-mail, écrivez à : zchatzid_at_dma.ens.fr.
|Orateur(s)||Franziska Jahnke - Münster,|
|Titre||Taming perfectoid fields|
|Horaire||11:00 à 12:30|
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).