CIRM - Videos & books Library - Residue field domination

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Auteurs : Haskell, Deirdre (Auteur de la conférence)
CIRM (Editeur )

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Résumé : The idea of stable domination for types in a theory was proposed and developed for algebraically closed valued ﬁelds in the eponymous book by Haskell, Hrushovski and Macpherson (2008). With the observation both that valued ﬁelds that are not algebraically closed generally have no stable part and that the stable part of an algebraically closed valued ﬁeld is closely linked to the residue ﬁeld, it seemed appropriate to consider a notion of residue ﬁeld domination. In this talk, I will illustrate the idea of residue ﬁeld domination with various examples, and then present some theorems which apply to some henselian valued ﬁelds of characteristic zero. These results are presented in a recent preprint of Ealy, Haskell and Simon, with similar results in a preprint of Vicaria.

Mots-Clés : valued fields; stable domination

Codes MSC :
03C60 - Model-theoretic algebra
12J10 - Valued fields
12L12 - Model theory

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Petit, Jean

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https://videos.cirm-math.fr/2023_05-30_Haskell_1.mp4

Informations sur la Rencontre

Nom de la Rencontre : Model theory of valued fields / Théorie des modèles des corps valués
Organisateurs de la Rencontre : Chatzidakis, Zoé ; Jahnke, Franziska ; Rideau-Kikuchi, Silvain
Dates : 29/05/2023 - 02/06/2023
Année de la rencontre : 2023
URL de la Rencontre : https://conferences.cirm-math.fr/2761.html

Données de citation

DOI : 10.24350/CIRM.V.20051703
Citer cette vidéo: Haskell, Deirdre (2023). Residue field domination. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20051703
URI : http://dx.doi.org/10.24350/CIRM.V.20051703

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Bibliographie

EALY, Clifton, HASKELL, Deirdre, et SIMON, Pierre. Residue field domination in some henselian valued fields. arXiv preprint arXiv:2212.05188, 2022. - https://doi.org/10.48550/arXiv.2212.05188

VICARIA, Mariana. Residue field domination in henselian valued fields of equicharacteristic zero. arXiv preprint arXiv:2109.08243, 2021. - https://doi.org/10.48550/arXiv.2109.08243

HASKELL, Deirdre, HRUSHOVSKI, Ehud, et MACPHERSON, Dugald. Stable domination and independence in algebraically closed valued fields. arXiv preprint math/0511310, 2005. - https://doi.org/10.48550/arXiv.math/0511310

EALY, Clifton, HASKELL, Deirdre, et MARIKOVA, Jana. Residue field domination in real closed valued fields. 2019. - https://doi.org/10.48550/arXiv.2109.08243

KOVACSICS, Pablo Cubides, HILS, Martin, et YE, Jinhe. Beautiful pairs. arXiv preprint arXiv:2112.00651, 2021. - https://doi.org/10.48550/arXiv.2112.00651

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