Français
Multi topological fields and NTP2
Multi angle
Authors : Montenegro Guzman, Samaria (Author of the conference)
CIRM (Publisher )
03C40 - Interpolation, preservation, definability
03C98 - Applications of model theory
12J10 - Valued fields
12J15 - Ordered fields
12L12 - Model theory
CIRM (Publisher )
Loading the player...
|
Abstract :
Joint work with Silvain Rideau-Kikuchi.
Pseudo algebraically closed, pseudo real closed, and pseudo p-adically closed fields are examples of unstable fields that share many similarities, but have mostly been studied separately. In this talk, we propose a unified framework for studying them: the class of pseudo $T$ -closed fields, where $T$ is an enriched theory of fields. These fields verify a 'local-global' principle for the existence of points on varieties with respect to models of $T$ . This approach also enables a good description of some fields equipped with multiple V -topologies, particularly pseudo algebraically closed fields with a finite number of valuations. An important result that will be discussed in this talk is a (model theoretic) classification theorem for bounded pseudo T -closed fields, in particular we show that under specific hypotheses on $T$ , these fields are NTP2 of finite burden.
Keywords : model theory; valued fields; ordered fields; NTP2; PAC; PRC; PpC fields
MSC Codes : Pseudo algebraically closed, pseudo real closed, and pseudo p-adically closed fields are examples of unstable fields that share many similarities, but have mostly been studied separately. In this talk, we propose a unified framework for studying them: the class of pseudo $T$ -closed fields, where $T$ is an enriched theory of fields. These fields verify a 'local-global' principle for the existence of points on varieties with respect to models of $T$ . This approach also enables a good description of some fields equipped with multiple V -topologies, particularly pseudo algebraically closed fields with a finite number of valuations. An important result that will be discussed in this talk is a (model theoretic) classification theorem for bounded pseudo T -closed fields, in particular we show that under specific hypotheses on $T$ , these fields are NTP2 of finite burden.
Keywords : model theory; valued fields; ordered fields; NTP2; PAC; PRC; PpC fields
03C40 - Interpolation, preservation, definability
03C98 - Applications of model theory
12J10 - Valued fields
12J15 - Ordered fields
12L12 - Model theory
|
Information on the Video
Film maker : Petit, JeanLanguage : English Available date : 23/06/2023 Conference Date : 30/05/2023 Subseries : Research talks arXiv category : Logic Mathematical Area(s) : Algebra ; Logic and Foundations Format : MP4 (.mp4) - HD Video Time : 00:48:56 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023_05-30_Montenegro_.mp4 
|
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.20052903Cite this video as: Montenegro Guzman, Samaria (2023). Multi topological fields and NTP2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20052903 URI : http://dx.doi.org/10.24350/CIRM.V.20052903 |
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] 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] Beyond the Fontaine-Wintenberger theorem / Author of the conference Kartas, Konstantinos.
- [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
- MONTENEGRO, Samaria et RIDEAU-KIKUCHI, Silvain. Pseudo T-closed fields. arXiv preprint arXiv:2304.10433, 2023. - https://doi.org/10.48550/arXiv.2304.10433
Imagette Video
