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Existential closedness of $\mathbb{Q}^{alg}$ as a globally valued field
Multi angle
Authors : Szachniewicz, Michal (Author of the conference)
CIRM (Publisher )
03C10 - Quantifier elimination and related topics
14G35 - Modular and Shimura varieties
32U35 - Plurisubharmonic extremal functions, pluricomplex Green functions
Additional resources :
https://webusers.imj-prg.fr/~zoe.chatzidakis/CIRM/Szachniewicz.pdf
CIRM (Publisher )
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Abstract :
I will talk about an application of the differentiability of the arithmetic volume function and an arithmetic Bertini type theorem to classify when one can find a closed point on the generic fiber of an arithmetic variety, whose heights with respect to some finite tuple of arithmetic R-divisors approximate a given tuple of real numbers.This result is used to prove existential closedness of $\mathbb{Q}^{alg}$ as a globally valued field (abbreviated GVF) - it is an arithmetic analogue of the function field case published recently by Ita Ben Yaacov and Ehud Hrushovski.
Keywords : logic; Arakelov geometry; unbounded continuous logic
MSC Codes : Keywords : logic; Arakelov geometry; unbounded continuous logic
03C10 - Quantifier elimination and related topics
14G35 - Modular and Shimura varieties
32U35 - Plurisubharmonic extremal functions, pluricomplex Green functions
Additional resources :
https://webusers.imj-prg.fr/~zoe.chatzidakis/CIRM/Szachniewicz.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 23/06/2023 Conference Date : 30/05/2023 arXiv category : Logic ; Algebraic Geometry Mathematical Area(s) : Algebraic & Complex Geometry ; Logic and Foundations ; Number Theory Format : MP4 (.mp4) - HD Video Time : 00:42:13 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023_05-30_Szachniewicz.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.20053503Cite this video as: Szachniewicz, Michal (2023). Existential closedness of $\mathbb{Q}^{alg}$ as a globally valued field. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20053503 URI : http://dx.doi.org/10.24350/CIRM.V.20053503 |
See Also
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Bibliography
- YAACOV, Itaï Ben et HRUSHOVSKI, Ehud. Globally valued function fields: existential closure. arXiv preprint arXiv:2212.07269, 2022. - https://doi.org/10.48550/arXiv.2212.07269
- WILMS, Robert. On the Irreducibility and Distribution of Arithmetic Divisors. arXiv preprint arXiv:2211.03766, 2022. - https://doi.org/10.48550/arXiv.2211.03766
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