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Beyond the Fontaine-Wintenberger theorem

By Konstantinos Kartas

Appears in collection : Model theory of valued fields / Théorie des modèles des corps valués

Given a perfectoid field, we find an elementary extension and an especially nice valuation on it whose residue field is an elementary extension of the tilt. This specializes to the almost purity theorem over perfectoid valuation rings and Fontaine-Wintenberger. Along the way, we prove an Ax-Kochen/Ershov principle for certain deeply ramified fields, which also uncovers some new model-theoretic phenomena in positive characteristic. Notably, we get that the perfect hull of $\mathbb{F}_p(t)^h$ is an elementary substructure of the perfect hull of $\mathbb{F}_p((t))$. Joint work with Franziska Jahnke.

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Citation data

  • DOI 10.24350/CIRM.V.20052303
  • Cite this video Kartas Konstantinos (5/29/23). Beyond the Fontaine-Wintenberger theorem. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20052303
  • URL https://dx.doi.org/10.24350/CIRM.V.20052303


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