|Location:||MSRI: Simons Auditorium, Online/Virtual|
Model Theory Of 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. This is joint work with Konstantinos Kartas.