English
Beautiful pairs revisited
Multi angle
Auteurs : Ye, Jinhe (Auteur de la Conférence)
CIRM (Editeur )
03C10 - Quantifier elimination and related topics
03C45 - Classification theory, stability and related concepts [See also 03C48]
03C64 - Model theory of ordered structures; o-minimality
12J10 - Valued fields
12L12 - Model theory
CIRM (Editeur )
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Résumé :
We extend the notion of beautiful pairs by Poizat to unstable theories via definable types, with a specific interest in such pairs of valued fields. In particular, we establish an analogue of Ax-Kochen-Ershov principles in for certain pairs of valued fields. In the specific case of ACVF, we classify all such pairs and deduce the strict pro-definability of various spaces of definable types, such as the stable completion introduced by Hrushovski-Loeser and a model theoretic analogue of the Huber analytification of an algebraic variety. This is joint with Pablo Cubides Kovacsics and Martin Hils.
Keywords : beautiful pairs; valued fields; pro-definability; Ax-Kochen-Ershov principle
Codes MSC : Keywords : beautiful pairs; valued fields; pro-definability; Ax-Kochen-Ershov principle
03C10 - Quantifier elimination and related topics
03C45 - Classification theory, stability and related concepts [See also 03C48]
03C64 - Model theory of ordered structures; o-minimality
12J10 - Valued fields
12L12 - Model theory
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Informations sur la Vidéo
Réalisateur : Petit, JeanLangue : Anglais Date de publication : 23/06/2023 Date de captation : 30/05/2023 Sous collection : Research talks arXiv category : Logic Domaine : Logic and Foundations Format : MP4 (.mp4) - HD Durée : 00:56:16 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023_05-30_Ye_1.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Model theory of valued fields / Théorie des modèles des corps valuésOrganisateurs de la rencontre : Chatzidakis, Zoé ; Jahnke, Franziska ; Rideau-Kikuchi, Silvain Dates : 29/05/2023 - 02/06/2023 Année de la rencontre : 2023 URL Congrès : https://conferences.cirm-math.fr/2761.html
Données de citation
DOI : 10.24350/CIRM.V.20053903Citer cette vidéo: Ye, Jinhe (2023). Beautiful pairs revisited. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20053903 URI : http://dx.doi.org/10.24350/CIRM.V.20053903 |
Voir aussi
- [Multi angle] An Imaginary Ax-Kochen/Ershov principle: the equicharacteristic zero case / Auteur de la Conférence Vicaria, Mariana.
- [Multi angle] Existential closedness of $\mathbb{Q}^{alg}$ as a globally valued field / Auteur de la Conférence Szachniewicz, Michal.
- [Multi angle] Interpretable, definably semisimple groups in various valued fields / Auteur de la Conférence Peterzil, Ya'acov.
- [Multi angle] The existential closedness problem for analytic solutions of difference equations / Auteur de la Conférence Padgett, Adele.
- [Multi angle] Multi topological fields and NTP2 / Auteur de la Conférence Montenegro Guzman, Samaria.
- [Multi angle] A Hasse principle over Berkovich analytic curves / Auteur de la Conférence Mehmeti, Vlerë.
- [Multi angle] Definable convex and henselian valuations on ordered fields / Auteur de la Conférence Krapp, Lothar Sebastian.
- [Multi angle] Beyond the Fontaine-Wintenberger theorem / Auteur de la Conférence Kartas, Konstantinos.
- [Multi angle] Around NIP Noetherian domains / Auteur de la Conférence Johnson, Will.
- [Multi angle] An invitation to globally valued fields / Auteur de la Conférence Hrushovski, Ehud.
- [Multi angle] Lang-Weil type bounds in finite difference fields / Auteur de la Conférence Hils, Martin.
- [Multi angle] Residue field domination / Auteur de la Conférence Haskell, Deirdre.
- [Multi angle] Motivic integration with pseudo-finite residue field and fundamental lemma / Auteur de la Conférence Forey, Arthur.
- [Multi angle] Tropical functions on skeletons / Auteur de la Conférence Ducros, Antoine.
- [Multi angle] Contracting endomorphisms of valued fields / Auteur de la Conférence Dor, Yuval.
- [Multi angle] Ax-Kochen-Ershov principles for finitely ramified henselian fields / Auteur de la Conférence Dittmann, Philip.
- [Multi angle] Group construction in $C$-minimal structures / Auteur de la Conférence Delon, Françoise.
- [Multi angle] Homology groups in algebraically closed valued fields / Auteur de la Conférence Cubides Kovacsics, Pablo.
- [Multi angle] Existential uniform p-adic integration and descent for integrability and largest poles / Auteur de la Conférence Cluckers, Raf.
- [Multi angle] Polynomials that vanish on many sets of codimension 2 / Auteur de la Conférence Ben Yaacov, Itaï.
- [Multi angle] The model theory of Hardy fields and linear differential equations / Auteur de la Conférence Aschenbrenner, Matthias.
- [Multi angle] Transfer of decidability for existential theories of (valued) fields / Auteur de la Conférence Anscombe, Sylvy.
Bibliographie
- KOVACSICS, Pablo Cubides, HILS, Martin, et YE, Jinhe. Beautiful pairs. arXiv preprint arXiv:2112.00651, 2021. - https://doi.org/10.48550/arXiv.2112.00651
Imagette Video
