6 papers
Definability via the tilting correspondence
Gessica Alecci, Ihsane Hadeg, Franziska Jahnke +2
We show that arithmetic definability of henselian valuations is preserved by the tilting correspondence. Moreover, we show that if a perfectoid valuation is arithmetically definabl…
Perfectoid fields in the language of rings
Franziska Jahnke, Ferréol Lavaud
Building on work of the first author and Kartas, we identify the elementary class generated by all perfectoid fields of fixed residue characteristic in the language of rings.
AKE principles for deeply ramified fields
Franziska Jahnke, Jonas van der Schaaf
We study the model theory of deeply ramified fields of positive characteristic. Generalizing the perfect case treated in work by Jahnke and Kartas on the model theory of perfectoid…
Ax-Kochen-Ershov principles for finitely ramified henselian fields
Sylvy Anscombe, Philip Dittmann, Franziska Jahnke
We study the model theory of finitely ramified henselian valued fields of fixed initial ramification, obtaining versions of the Ax-Kochen-Ershov principle as follows. We identify t…
Growing Spines Ad Infinitum
Blaise Boissonneau, Anna De Mase, Franziska Jahnke +1
We show that every non-trivial ordered abelian group is augmentable by infinite elements, i.e., we have for some non-trivial ordered abelian group …
Beyond the Fontaine-Wintenberger theorem
Franziska Jahnke, Konstantinos Kartas
Given a perfectoid field, we find an elementary extension and a henselian defectless valuation on it, whose value group is divisible and whose residue field is an elementary extens…