The model theory of perfectoid fields [after Jahnke and Kartas]
Sylvy Anscombe
TL;DR
This paper discusses the model theory of perfectoid fields, focusing on recent advances by Jahnke and Kartas that extend classical theorems in the area, providing new insights into their structure.
Contribution
It analyzes the work of Jahnke and Kartas on perfectoid fields, highlighting their extensions beyond the Fontaine-Wintenberger theorem.
Findings
Extended the model-theoretic understanding of perfectoid fields
Connected model theory with recent advances in p-adic geometry
Provided new perspectives on the structure of perfectoid fields
Abstract
This text was written to support a Bourbaki seminar given in January 2026 on the subject of the model theory of perfectoid fields, especially on the work of Jahnke and Kartas in their paper "Beyond the Fontaine-Wintenberger theorem", J. Amer. Math. Soc. 38 (4), pp. 997-1047, 2025.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Algebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology