Existential closedness of $\mathbb{Q}^{alg}$ as a globally valued field

Apparaît dans la collection : Model theory of valued fields / Théorie des modèles des corps valués

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.

Informations sur la vidéo

Date de captation 30/05/2023
Date de publication 23/06/2023
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20053503
Citer cette vidéo Szachniewicz, Michal (30/05/2023). Existential closedness of $\mathbb{Q}^{alg}$ as a globally valued field. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20053503
URL https://dx.doi.org/10.24350/CIRM.V.20053503

Domaine(s)

Bibliographie

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