English
Around NIP Noetherian domains
Multi angle
Auteurs : Johnson, Will (Auteur de la Conférence)
CIRM (Editeur )
03C45 - Classification theory, stability and related concepts [See also 03C48]
03C60 - Model-theoretic algebra
Ressources complémentaires :
https://webusers.imj-prg.fr/~zoe.chatzidakis/CIRM/Johnson.pdf
CIRM (Editeur )
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Résumé :
Which Noetherian integral domains are NIP? This is a natural question to ask, given the prominence of Noetherian rings in commutative algebra. We cannot hope to answer this question in full generality any time soon, as it includes other hard problems such as the conjectures on stable fields and NIP fields. Nevertheless, we present some interesting partial results which begin to paint a picture of NIP Noetherian rings. Let $R$ be a Noetherian domain which is NIP. Then either $R$ is a field, or $R$ is a semilocal domain of Krull dimension 1 and characteristic 0. Assuming the henselianity conjecture on NIP valued fields, $R$ is a henselian local ring. In the dp-minimal case, one can give a complete classification. Specifically, every dp-minimal Noetherian domain is a finite index subring of a dp-minimal discrete valuation ring. The situation in dp-rank 2 seems to be significantly worse, but a classification may still be possible in terms of differential valued fields.
Codes MSC : 03C45 - Classification theory, stability and related concepts [See also 03C48]
03C60 - Model-theoretic algebra
Ressources complémentaires :
https://webusers.imj-prg.fr/~zoe.chatzidakis/CIRM/Johnson.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 23/06/2023 Date de captation : 30/05/2023 Sous collection : Research talks arXiv category : Logic ; Commutative Algebra Domaine : Algebra ; Logic and Foundations Format : MP4 (.mp4) - HD Durée : 01:08:01 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-06-01_Johnson_1.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Model theory of valued fields / Théorie des modèles des corps valuésOrganisateurs de la rencontre : Chatzidakis, Zoé ; Jahnke, Franziska ; Rideau-Kikuchi, Silvain Dates : 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.20052103Citer cette vidéo: Johnson, Will (2023). Around NIP Noetherian domains. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20052103 URI : http://dx.doi.org/10.24350/CIRM.V.20052103 |
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