English
Interpretable, definably semisimple groups in various valued fields
Multi angle
Auteurs : Peterzil, Ya'acov (Auteur de la Conférence)
CIRM (Editeur )
CIRM (Editeur )
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Résumé :
(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.
Codes MSC : 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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Informations sur la Vidéo
Réalisateur : Petit, JeanLangue : Anglais Date de publication : 23/06/2023 Date de captation : 31/05/2023 Sous collection : Research talks arXiv category : Logic Domaine : Logic and Foundations Format : MP4 (.mp4) - HD Durée : 01:05:07 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023_05-31_Peterzil.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.20053303Citer cette vidéo: 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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Bibliographie
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