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Residue field domination
Multi angle
Authors : Haskell, Deirdre (Author of the conference)
CIRM (Publisher )
03C60 - Model-theoretic algebra
12J10 - Valued fields
12L12 - Model theory
CIRM (Publisher )
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Abstract :
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
MSC Codes : Keywords : valued fields; stable domination
03C60 - Model-theoretic algebra
12J10 - Valued fields
12L12 - Model theory
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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 : 00:46:49 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023_05-30_Haskell_1.mp4 
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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.20051703Cite this video as: 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 |
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] Multi topological fields and NTP2 / Author of the conference Montenegro Guzman, Samaria.
- [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] 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
- 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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