English
Multi topological fields and NTP2
Multi angle
Auteurs : Montenegro Guzman, Samaria (Auteur de la Conférence)
CIRM (Editeur )
03C40 - Interpolation, preservation, definability
03C98 - Applications of model theory
12J10 - Valued fields
12J15 - Ordered fields
12L12 - Model theory
CIRM (Editeur )
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Résumé :
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
Codes MSC : 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
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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 : Algebra ; Logic and Foundations Format : MP4 (.mp4) - HD Durée : 00:48:56 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023_05-30_Montenegro_.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.20052903Citer cette vidéo: 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 |
Voir aussi
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- [Multi angle] The model theory of Hardy fields and linear differential equations / Auteur de la Conférence Aschenbrenner, Matthias.
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Bibliographie
- MONTENEGRO, Samaria et RIDEAU-KIKUCHI, Silvain. Pseudo T-closed fields. arXiv preprint arXiv:2304.10433, 2023. - https://doi.org/10.48550/arXiv.2304.10433
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