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An invitation to globally valued fields
Multi angle
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Abstract :
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
MSC Codes : Keywords : globally valued fields
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Information on the Video
Language : EnglishAvailable date : 23/06/2023 Conference Date : 29/05/2023 Subseries : Research talks arXiv category : Logic ; Algebraic Geometry Mathematical Area(s) : Geometry ; Logic and Foundations Format : MP4 (.mp4) - HD Video Time : 01:11:28 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-05-29_Hrushovski.mp4 
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Information on the Event
Event Title : Model theory of valued fields / Théorie des modèles des corps valuésDates : 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.20051903Cite this video as: (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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Bibliography
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