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.

Keywords : valued fields; stable domination

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

Informations sur la Vidéo

Réalisateur :

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 Congrès : 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

Voir aussi

[Multi angle] Beautiful pairs revisited / Auteur de la Conférence Ye, Jinhe.
[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] 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

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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