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H 1 Twisted Kac-Moody groups over the integers

Auteurs : Lourenço, João (Auteur de la Conférence)
CIRM (Editeur )

Résumé : In geometric representation theory, one is interested in studying the geometry of affine Grassmannians of quasi-split simply-connected reductive groups. In this endeavor, one of the main techniques, introduced by Faltings in the split case, consists in constructing natural realisations of these ind-schemes over the integers. In the twisted case, this was done by Pappas and Rapoport in the tamely ramified case, i.e. over $\mathbb{Z}[1/e]$, where $e = 2$ or $3$ is the order of the automorphism group of the split form we are dealing with. We explain how to extend the parahoric group scheme that appeared in work of Pappas, Rapoport, Tits and Zhu to the polynomial ring $\mathbb{Z}[t]$ with integer coefficients and additionally how the group scheme obtained in char. $e$ can be regarded as a parahoric model of a basic exotic pseudo-reductive group. Then we study the geometry of the affine Grassmannian and also its global deformation à la Beilinson-Drinfeld, recovering all the known results in the literature away from $e = 0$. This also has some pertinence to the study of local models of Shimura varieties in wildly ramified cases.

Keywords : Kac-Moody groups; Hecke algebras

Codes MSC :
20C08 - Hecke algebras and their representations
20G44 - Kac-Moody groups

 Informations sur la Vidéo Réalisateur : Hennenfent, Guillaume Langue : Anglais Date de publication : 20/09/2019 Date de captation : 30/08/2019 Collection : Research talks ; Algebraic and Complex Geometry ; Number Theory Format : MP4 Durée : 00:54:24 Domaine : Number Theory ; Algebraic & Complex Geometry Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2019-08-30_Lourenço.mp4 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, NicolasDates : 26/08/2019 - 06/09/2019 Année de la rencontre : 2019 URL Congrès : https://conferences.cirm-math.fr/2067.htmlCitation Data DOI : 10.24350/CIRM.V.19559403 Cite this video as: Lourenço, João (2019). Twisted Kac-Moody groups over the integers. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19559403 URI : http://dx.doi.org/10.24350/CIRM.V.19559403

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