English
Homology groups in algebraically closed valued fields
Multi angle
Auteurs : Cubides Kovacsics, Pablo (Auteur de la Conférence)
CIRM (Editeur )
03C64 - Model theory of ordered structures; o-minimality
03C98 - Applications of model theory
12J25 - Non-Archimedean valued fields, See also {30G06, 32P05, 46S10, 47S10}
55N35 - Other homology theories
CIRM (Editeur )
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Résumé :
In his PhD thesis, A. Woerheide constructed well-behaved homology groups for definable sets in o-minimal expansions of real closed fields. The question arises whether such groups exist in o-minimal reducts, such as ordered vector spaces over ordered division rings. Why is this question interesting? A positive answer, combined with the work of Hrushovski-Loeser on stable completions, forms the basis for defining homology groups of definable sets in algebraically closed valued fields (ACVF). As an application, one can recover and extend results of S. Basu and D. Patel concerning uniform bounds of Betti numbers in ACVF. In this talk, I will present results and advancements on this topic. This is an ongoing joint work with Mario Edmundo, Pantelis Eleftheriou and Jinhe Ye.
Keywords : homology; algebraically closed valued fields; rigid analytic spaces; o-minimality; tropical homology
Codes MSC : Keywords : homology; algebraically closed valued fields; rigid analytic spaces; o-minimality; tropical homology
03C64 - Model theory of ordered structures; o-minimality
03C98 - Applications of model theory
12J25 - Non-Archimedean valued fields, See also {30G06, 32P05, 46S10, 47S10}
55N35 - Other homology theories
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 23/06/2023 Date de captation : 01/06/2023 Sous collection : Research talks arXiv category : Algebraic Geometry ; Algebraic Topology ; Logic Domaine : Algebra ; Geometry ; Logic and Foundations Format : MP4 (.mp4) - HD Durée : 01:03:45 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-06-01_Kovacsis.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.20050803Citer cette vidéo: Cubides Kovacsics, Pablo (2023). Homology groups in algebraically closed valued fields. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20050803 URI : http://dx.doi.org/10.24350/CIRM.V.20050803 |
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] Residue field domination / Auteur de la Conférence Haskell, Deirdre.
- [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] 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
- BASU, Saugata et PATEL, Deepam. VC density of definable families over valued fields. Journal of the European Mathematical Society, 2021, vol. 23, no 7, p. 2361-2403. - https://doi.org/10.4171/jems/1056
- HRUSHOVSKI, Ehud et LOESER, François. Non-Archimedean Tame Topology and Stably Dominated Types (AM-192). Princeton University Press, 2016. -
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