Beyond the Fontaine-Wintenberger theorem | Vidéo | Carmin.tv

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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.

Information about the video

Date of recording 29/05/2023
Date of publication 23/06/2023
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20052303
Cite this video Kartas, Konstantinos (29/05/2023). Beyond the Fontaine-Wintenberger theorem. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20052303
URL https://dx.doi.org/10.24350/CIRM.V.20052303

Domain(s)

Bibliography

JAHNKE, Franziska et KARTAS, Konstantinos. Beyond the Fontaine-Wintenberger theorem. arXiv preprint arXiv:2304.05881, 2023. - https://doi.org/10.48550/arXiv.2304.05881

MSC codes

Document(s)

https://webusers.imj-prg.fr/~zoe.chatzidakis/CIRM/Kartas.pdf

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