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Descent in Bruhat-Tits theory
Post-edited
Authors : Prasad, Gopal (Author of the conference)
CIRM (Publisher )
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 (Publisher )
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| reductive groups Bruhat-Tits theory unramified descent |
Abstract :
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
MSC Codes : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 20/09/2019 Conference Date : 28/08/2019 Subseries : Research School arXiv category : Group Theory Mathematical Area(s) : Algebraic & Complex Geometry ; Lie Theory and Generalizations ; Number Theory Format : MP4 (.mp4) - HD Video Time : 01:33:03 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-08-28_G_Prasad.mp4 
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Information on the Event
Event Title : Buildings and Affine Grassmannians / Immeubles et grassmanniennes affinesEvent Organizers : Fauquant-Millet, Florence ; Fedorov, Roman ; Gille, Philippe ; Loisel, Benoît ; Ressayre, Nicolas Dates : 26/08/2019 - 06/09/2019 Event Year : 2019 Event URL : https://conferences.cirm-math.fr/2067.html
Citation Data
DOI : 10.24350/CIRM.V.19559103Cite this video as: 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 |
See Also
- [Multi angle] Twisted Kac-Moody groups over the integers / Author of the conference Lourenço, João.
- [Multi angle] Point de vue de Berkovich sur l'immeuble et filtrations / Author of the conference Mayeux, Arnaud.
- [Multi angle] Basics on affine Grassmanianns / Author of the conference Richarz, Timo.
- [Multi angle] Bruhat-Tits theory of quasi-split groups / Author of the conference Rémy, Bertrand.
Bibliography
- PRASAD, Gopal. A new approach to unramified descent in Bruhat-Tits theory. arXiv preprint arXiv:1611.07430, 2016. - https://arxiv.org/abs/1611.07430
