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Homology groups in algebraically closed valued fields
Multi angle
Authors : Cubides Kovacsics, Pablo (Author of the conference)
CIRM (Publisher )
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 (Publisher )
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Abstract :
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
MSC Codes : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 23/06/2023 Conference Date : 01/06/2023 Subseries : Research talks arXiv category : Algebraic Geometry ; Algebraic Topology ; Logic Mathematical Area(s) : Algebra ; Geometry ; Logic and Foundations Format : MP4 (.mp4) - HD Video Time : 01:03:45 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-06-01_Kovacsis.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.20050803Cite this video as: 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 |
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] Residue field domination / Author of the conference Haskell, Deirdre.
- [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] 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
- 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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