English
Descent in Bruhat-Tits theory
Post-edited
Auteurs : Prasad, Gopal (Auteur de la Conférence)
CIRM (Editeur )
20E42 - Groups with a $BN$-pair; buildings, See also {51E24}
20G15 - Linear algebraic groups over arbitrary fields
51E24 - Buildings and the geometry of diagrams
CIRM (Editeur )
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| reductive groups Bruhat-Tits theory unramified descent |
Résumé :
Bruhat-Tits theory applies to a semisimple group G, defined over an henselian discretly valued field K, such that G admits a Borel K-subgroup after an extension of K. The construction of the theory goes then by a deep Galois descent argument for the building and also for the parahoric group scheme. In the case of unramified extension, that descent has been achieved by Bruhat-Tits at the end of [BT2]. The tamely ramified case is due to G. Rousseau [R]. Recently, G. Prasad found a new way to investigate the descent part of the theory. This is available in the preprints [Pr1, Pr2] dealing respectively with the unramified case and the tamely ramified case. It is much shorter and the method is based more on fine geometry of the building (e.g. galleries) than algebraic groups techniques.
Keywords : linear algebraic groups; buildings
Codes MSC : Keywords : linear algebraic groups; buildings
20E42 - Groups with a $BN$-pair; buildings, See also {51E24}
20G15 - Linear algebraic groups over arbitrary fields
51E24 - Buildings and the geometry of diagrams
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 20/09/2019 Date de captation : 28/08/2019 Sous collection : Research School arXiv category : Group Theory Domaine : Algebraic & Complex Geometry ; Lie Theory and Generalizations ; Number Theory Format : MP4 (.mp4) - HD Durée : 01:33:03 Audience : Researchers Download : https://videos.cirm-math.fr/2019-08-28_G_Prasad.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Buildings and Affine Grassmannians / Immeubles et grassmanniennes affinesOrganisateurs de la rencontre : Fauquant-Millet, Florence ; Fedorov, Roman ; Gille, Philippe ; Loisel, Benoît ; Ressayre, Nicolas Dates : 26/08/2019 - 06/09/2019 Année de la rencontre : 2019 URL Congrès : https://conferences.cirm-math.fr/2067.html
Données de citation
DOI : 10.24350/CIRM.V.19559103Citer cette vidéo: Prasad, Gopal (2019). Descent in Bruhat-Tits theory. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19559103 URI : http://dx.doi.org/10.24350/CIRM.V.19559103 |
Voir aussi
- [Multi angle] Twisted Kac-Moody groups over the integers / Auteur de la Conférence Lourenço, João.
- [Multi angle] Point de vue de Berkovich sur l'immeuble et filtrations / Auteur de la Conférence Mayeux, Arnaud.
- [Multi angle] Basics on affine Grassmanianns / Auteur de la Conférence Richarz, Timo.
- [Multi angle] Bruhat-Tits theory of quasi-split groups / Auteur de la Conférence Rémy, Bertrand.
Bibliographie
- PRASAD, Gopal. A new approach to unramified descent in Bruhat-Tits theory. arXiv preprint arXiv:1611.07430, 2016. - https://arxiv.org/abs/1611.07430
