Model theory of valued fields / Théorie des modèles des corps valués

Collection Model theory of valued fields / Théorie des modèles des corps valués

Organizer(s) Chatzidakis, Zoé ; Jahnke, Franziska ; Rideau-Kikuchi, Silvain

Date(s) 29/05/2023 - 02/06/2023

linked URL https://conferences.cirm-math.fr/2761.html

00:00:00 / 00:00:00

15 23

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

By Michal Szachniewicz

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.

Information about the video

Date of recording 30/05/2023
Date of publication 23/06/2023
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20053503
Cite this video 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

Domain(s)

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

MSC codes

Document(s)

https://webusers.imj-prg.fr/~zoe.chatzidakis/CIRM/Szachniewicz.pdf

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow

All the collection videos

57:48

published on June 23, 2023

Tropical functions on skeletons

By Antoine Ducros

58:31

published on June 23, 2023

Motivic integration with pseudo-finite residue field and fundamental lemma

By Arthur Forey

01:11:28

published on June 23, 2023

An invitation to globally valued fields

By Ehud Hrushovski

01:01:18

published on June 23, 2023

Beyond the Fontaine-Wintenberger theorem

By Konstantinos Kartas

01:01:25

published on June 23, 2023

A Hasse principle over Berkovich analytic curves

By Vlerë Mehmeti

53:56

published on June 23, 2023

Contracting endomorphisms of valued fields

By Yuval Dor

01:08:40

published on June 23, 2023

Group construction in $C$-minimal structures

By Françoise Delon

01:02:55

Transfer of decidability for existential theories of (valued) fields

By Sylvy Anscombe

01:00:16

published on June 23, 2023

Existential uniform p-adic integration and descent for integrability and largest poles

By Raf Cluckers

01:08:01

published on June 23, 2023

Around NIP Noetherian domains

By Will Johnson

01:03:45

published on June 23, 2023

Homology groups in algebraically closed valued fields

By Pablo Cubides Kovacsics

01:03:54

published on June 23, 2023

Definable convex and henselian valuations on ordered fields

By Lothar Sebastian Krapp

46:49

published on June 23, 2023

Residue field domination

By Deirdre Haskell

01:07:10

published on June 23, 2023

Lang-Weil type bounds in finite difference fields

By Martin Hils

$Existential closedness of $\mathbb{Q}^{alg}$ as a globally valued field$
42:06

published on June 23, 2023

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

By Michal Szachniewicz

56:16

published on June 23, 2023

Beautiful pairs revisited

By Jinhe Ye

01:05:07

published on June 23, 2023

Interpretable, definably semisimple groups in various valued fields

By Ya'acov Peterzil

56:37

published on June 23, 2023

An Imaginary Ax-Kochen/Ershov principle: the equicharacteristic zero case

By Mariana Vicaria

01:07:38

published on June 23, 2023

The model theory of Hardy fields and linear differential equations

By Matthias Aschenbrenner

01:01:27

published on June 23, 2023

Polynomials that vanish on many sets of codimension 2

By Itaï Ben Yaacov

01:00:12

published on June 23, 2023

Ax-Kochen-Ershov principles for finitely ramified henselian fields

By Philip Dittmann

01:00:14

published on June 23, 2023

The existential closedness problem for analytic solutions of difference equations

By Adele Padgett

48:56

published on June 23, 2023

Multi topological fields and NTP2

By Samaria Montenegro Guzman

Copyright Carmin.tv 2024

Give feedback