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Seminar

Model Theory of Perfectoid Fields July 18, 2022 (02:15 PM PDT - 03:00 PM PDT)
Parent Program:
Location: MSRI: Simons Auditorium, Online/Virtual
Speaker(s) Franziska Jahnke (Westfälische Wilhelms-Universität Münster)
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Model Theory Of Perfectoid Fields

Abstract/Media

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.

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Model Theory Of Perfectoid Fields