English
An invitation to globally valued fields
Multi angle
Auteurs : ... (Auteur de la Conférence)
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Résumé :
The model theory of valued fields usually concerns a single valuation, or a family of independent valuations. But many phenomena of geometry and number theory are ‘global' in nature and invisible to any finite number of places. Much is ultimately based on a single relation among the different valuations and absolute values, the product formula. This formula can be axiomatized within continuous logic as the theory GVF. I will describe some of what we know and some of what we don't know about this theory. In particular I hope to reach the role of certain type-definable subgroups of abelian varieties, intriguingly analogous to Manin kernels in differential algebra, the associated interpretable Hilbert spaces, the Hodge index theorem, and their roles in proving stability of certain fragments. This will be in part introductory, and in part complementary, to talks by Ben Yaacov and Szachniewicz.
Keywords : globally valued fields
Codes MSC : Keywords : globally valued fields
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Informations sur la Vidéo
Langue : AnglaisDate de publication : 23/06/2023 Date de captation : 29/05/2023 Sous collection : Research talks arXiv category : Logic ; Algebraic Geometry Domaine : Geometry ; Logic and Foundations Format : MP4 (.mp4) - HD Durée : 01:11:28 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-05-29_Hrushovski.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Model theory of valued fields / Théorie des modèles des corps valuésDates : 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.20051903Citer cette vidéo: (2023). An invitation to globally valued fields. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20051903 URI : http://dx.doi.org/10.24350/CIRM.V.20051903 |
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