English
An Imaginary Ax-Kochen/Ershov principle: the equicharacteristic zero case
Multi angle
Auteurs : Vicaria, Mariana (Auteur de la Conférence)
CIRM (Editeur )
03C60 - Model-theoretic algebra
Ressources complémentaires :
https://webusers.imj-prg.fr/~zoe.chatzidakis/CIRM/Vicaria.pdf
CIRM (Editeur )
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Résumé :
(joint with Rideau-Kikuchi)
One of the most striking results of the model theory of henselian valued fields is the Ax-Kochen/Ershov principle, which roughly states that the first order theory of a henselian valued field that is unramified is completely determined by the first order theory of its residue field and the first order theory of its value group. Our leading question is: Can one obtain an Imaginary Ax-Kochen/Ershov principle? In previous work, I showed that the complexity of the value group requires adding the stabilizer sorts. In previous work, Hils and Rideau-Kikuchi showed that the complexity of the residue field reflects by adding the interpretable sets of the linear sorts. In this talk we present recent results on weak elimination of imaginaries that combine both strategies for a large class of henselian valued fields of equicharacteristic zero. Examples include, among others, henselian valued fields with bounded galois group and henselian valued fields whose value group has bounded regular rank (with an angular component map).
Keywords : imaginaries; henselian valued fields
Codes MSC : One of the most striking results of the model theory of henselian valued fields is the Ax-Kochen/Ershov principle, which roughly states that the first order theory of a henselian valued field that is unramified is completely determined by the first order theory of its residue field and the first order theory of its value group. Our leading question is: Can one obtain an Imaginary Ax-Kochen/Ershov principle? In previous work, I showed that the complexity of the value group requires adding the stabilizer sorts. In previous work, Hils and Rideau-Kikuchi showed that the complexity of the residue field reflects by adding the interpretable sets of the linear sorts. In this talk we present recent results on weak elimination of imaginaries that combine both strategies for a large class of henselian valued fields of equicharacteristic zero. Examples include, among others, henselian valued fields with bounded galois group and henselian valued fields whose value group has bounded regular rank (with an angular component map).
Keywords : imaginaries; henselian valued fields
03C60 - Model-theoretic algebra
Ressources complémentaires :
https://webusers.imj-prg.fr/~zoe.chatzidakis/CIRM/Vicaria.pdf
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Informations sur la Vidéo
Réalisateur : Petit, JeanLangue : Anglais Date de publication : 23/06/2023 Date de captation : 31/05/2023 Sous collection : Research talks arXiv category : Logic Domaine : Algebra ; Logic and Foundations Format : MP4 (.mp4) - HD Durée : 00:56:37 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023_05-31_Vicaria_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.20053703Citer cette vidéo: Vicaria, Mariana (2023). An Imaginary Ax-Kochen/Ershov principle: the equicharacteristic zero case. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20053703 URI : http://dx.doi.org/10.24350/CIRM.V.20053703 |
Voir aussi
- [Multi angle] Beautiful pairs revisited / Auteur de la Conférence Ye, Jinhe.
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- [Multi angle] Multi topological fields and NTP2 / Auteur de la Conférence Montenegro Guzman, Samaria.
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- [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.
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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
- HILS, Martin et RIDEAU-KIKUCHI, Silvain. Un principe d'Ax-Kochen-Ershov imaginaire. arXiv preprint arXiv:2109.12189, 2021. - https://doi.org/10.48550/arXiv.2109.12189
- VICARÍA, Mariana. Elimination of imaginaries in C ((Γ)) $\mathbb {C}((\Gamma)) $. Journal of the London Mathematical Society, 2023. - http:// https://doi.org/10.1112/jlms.12751
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