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Interpretable, definably semisimple groups in various valued fields
Multi angle
Authors : Peterzil, Ya'acov (Author of the conference)
CIRM (Publisher )
CIRM (Publisher )
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Abstract :
(joint with Yatir Halevi and Assaf Hasson)
We continue our study of interpretable groups in various valued fields (e.g. RCVF, ACVF and $p$-adically closed fields), and show that if $G$ is an interpretable definably semisimple group, namely has no definable infinite normal abelian subgroup, then, up to a finite index subgroup, it is definably isogenous to a $G_1 \times G_2$, where $G 1$ and $G 2$ are $K$-linear and $k$-linear groups, respectively $(K=$ the valued field and $k=$ the residue field). As in our previous works, we analyze the groups via the 4 distinguished sorts: $K, k, \Gamma$ (value group) and $K / \mathcal{O}$ (the closed 0 -balls), and show that the sorts $\Gamma$ and $K / \mathcal{O}$ do not appear when $G$ is definably semisimple.
MSC Codes : We continue our study of interpretable groups in various valued fields (e.g. RCVF, ACVF and $p$-adically closed fields), and show that if $G$ is an interpretable definably semisimple group, namely has no definable infinite normal abelian subgroup, then, up to a finite index subgroup, it is definably isogenous to a $G_1 \times G_2$, where $G 1$ and $G 2$ are $K$-linear and $k$-linear groups, respectively $(K=$ the valued field and $k=$ the residue field). As in our previous works, we analyze the groups via the 4 distinguished sorts: $K, k, \Gamma$ (value group) and $K / \mathcal{O}$ (the closed 0 -balls), and show that the sorts $\Gamma$ and $K / \mathcal{O}$ do not appear when $G$ is definably semisimple.
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Information on the Video
Film maker : Petit, JeanLanguage : English Available date : 23/06/2023 Conference Date : 31/05/2023 Subseries : Research talks arXiv category : Logic Mathematical Area(s) : Logic and Foundations Format : MP4 (.mp4) - HD Video Time : 01:05:07 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023_05-31_Peterzil.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.20053303Cite this video as: Peterzil, Ya'acov (2023). Interpretable, definably semisimple groups in various valued fields. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20053303 URI : http://dx.doi.org/10.24350/CIRM.V.20053303 |
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Bibliography
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