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H 1 Twisted Kac-Moody groups over the integers

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

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    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

      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 affines
    Organisateurs 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

    Citation 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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