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Beyond the Fontaine-Wintenberger theorem
Multi angle
Authors : Kartas, Konstantinos (Author of the conference)
CIRM (Publisher )
03C60 - Model-theoretic algebra
12L12 - Model theory
16W60 - Filtrations and valuations, generalizations of Euclidean algorithm, completions, formal power series and related constructions, See also {13Jxx}
Additional resources :
https://webusers.imj-prg.fr/~zoe.chatzidakis/CIRM/Kartas.pdf
CIRM (Publisher )
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Abstract :
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.
Keywords : perfectoid fields; model theory; almost mathematics
MSC Codes : Keywords : perfectoid fields; model theory; almost mathematics
03C60 - Model-theoretic algebra
12L12 - Model theory
16W60 - Filtrations and valuations, generalizations of Euclidean algorithm, completions, formal power series and related constructions, See also {13Jxx}
Additional resources :
https://webusers.imj-prg.fr/~zoe.chatzidakis/CIRM/Kartas.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 23/06/2023 Conference Date : 29/05/2023 Subseries : Research talks arXiv category : Commutative Algebra ; Logic Mathematical Area(s) : Algebra ; Logic and Foundations ; Number Theory Format : MP4 (.mp4) - HD Video Time : 01:01:18 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-05-29_Kartas.mp4 
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Information on the Event
Event Title : Model theory of valued fields / Théorie des modèles des corps valuésEvent Organizers : Chatzidakis, Zoé ; Jahnke, Franziska ; Rideau-Kikuchi, Silvain Dates : 29/05/2023 - 02/06/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2761.html
Citation Data
DOI : 10.24350/CIRM.V.20052303Cite this video as: Kartas, Konstantinos (2023). Beyond the Fontaine-Wintenberger theorem. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20052303 URI : http://dx.doi.org/10.24350/CIRM.V.20052303 |
See Also
- [Multi angle] Beautiful pairs revisited / Author of the conference Ye, Jinhe.
- [Multi angle] An Imaginary Ax-Kochen/Ershov principle: the equicharacteristic zero case / Author of the conference Vicaria, Mariana.
- [Multi angle] Existential closedness of $\mathbb{Q}^{alg}$ as a globally valued field / Author of the conference Szachniewicz, Michal.
- [Multi angle] Interpretable, definably semisimple groups in various valued fields / Author of the conference Peterzil, Ya'acov.
- [Multi angle] The existential closedness problem for analytic solutions of difference equations / Author of the conference Padgett, Adele.
- [Multi angle] Multi topological fields and NTP2 / Author of the conference Montenegro Guzman, Samaria.
- [Multi angle] A Hasse principle over Berkovich analytic curves / Author of the conference Mehmeti, Vlerë.
- [Multi angle] Definable convex and henselian valuations on ordered fields / Author of the conference Krapp, Lothar Sebastian.
- [Multi angle] Around NIP Noetherian domains / Author of the conference Johnson, Will.
- [Multi angle] An invitation to globally valued fields / Author of the conference Hrushovski, Ehud.
- [Multi angle] Lang-Weil type bounds in finite difference fields / Author of the conference Hils, Martin.
- [Multi angle] Residue field domination / Author of the conference Haskell, Deirdre.
- [Multi angle] Motivic integration with pseudo-finite residue field and fundamental lemma / Author of the conference Forey, Arthur.
- [Multi angle] Tropical functions on skeletons / Author of the conference Ducros, Antoine.
- [Multi angle] Contracting endomorphisms of valued fields / Author of the conference Dor, Yuval.
- [Multi angle] Ax-Kochen-Ershov principles for finitely ramified henselian fields / Author of the conference Dittmann, Philip.
- [Multi angle] Group construction in $C$-minimal structures / Author of the conference Delon, Françoise.
- [Multi angle] Homology groups in algebraically closed valued fields / Author of the conference Cubides Kovacsics, Pablo.
- [Multi angle] Existential uniform p-adic integration and descent for integrability and largest poles / Author of the conference Cluckers, Raf.
- [Multi angle] Polynomials that vanish on many sets of codimension 2 / Author of the conference Ben Yaacov, Itaï.
- [Multi angle] The model theory of Hardy fields and linear differential equations / Author of the conference Aschenbrenner, Matthias.
- [Multi angle] Transfer of decidability for existential theories of (valued) fields / Author of the conference Anscombe, Sylvy.
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
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