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Around NIP Noetherian domains
Multi angle
Authors : Johnson, Will (Author of the conference)
CIRM (Publisher )
03C45 - Classification theory, stability and related concepts [See also 03C48]
03C60 - Model-theoretic algebra
Additional resources :
https://webusers.imj-prg.fr/~zoe.chatzidakis/CIRM/Johnson.pdf
CIRM (Publisher )
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Abstract :
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.
MSC Codes : 03C45 - Classification theory, stability and related concepts [See also 03C48]
03C60 - Model-theoretic algebra
Additional resources :
https://webusers.imj-prg.fr/~zoe.chatzidakis/CIRM/Johnson.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 23/06/2023 Conference Date : 30/05/2023 Subseries : Research talks arXiv category : Logic ; Commutative Algebra Mathematical Area(s) : Algebra ; Logic and Foundations Format : MP4 (.mp4) - HD Video Time : 01:08:01 Targeted 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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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.20052103Cite this video as: 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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Bibliography
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