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THÉORIE DE BRUHAT-TITS POUR LES GROUPES QUASI-RÉDUCTIFS

Part of: Algebraic groups Linear algebraic groups and related topics Special varieties Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  25 January 2021

João Lourenço Open the ORCID record for João Lourenço [Opens in a new window]
João Lourenço*
Affiliation:
Mathematisches Institut der Universität Bonn, Endenicher Allee 60, 53115Bonn, Deutschland ([email protected])
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Abstract

Soient K un corps discrètement valué et hensélien, ${\mathcal {O}}$ son anneau d’entiers supposé excellent, $\kappa $ son corps résiduel supposé parfait et G un K-groupe quasi-réductif, c’est-à-dire lisse, affine, connexe et à radical unipotent déployé trivial. On construit l’immeuble de Bruhat-Tits ${\mathcal {I}}(G, K)$ pour $G(K)$ de façon canonique, améliorant les constructions moins canoniques de M. Solleveld sur les corps locaux, et l’on associe un ${\mathcal {O}}$ -modèle en groupes ${\mathcal {G}}_{\Omega }$ de G à chaque partie non vide et bornée $\Omega $ contenue dans un appartement de ${\mathcal {I}}(G,K)$ . On montre que les groupes parahoriques ${\mathcal {G}}_{\textbf {f}}$ attachés aux facettes peuvent être caractérisés en fonction de la géométrie de leurs grassmanniennes affines, ainsi que dans la thèse de T. Richarz. Ces résultats sont appliqués ailleurs à l’étude des grassmanniennes affines tordues entières.

Keywords

grassmanniennes affinesschémas en groupesthéorie de Bruhat-Titsgroupes parahoriquesgroupes pseudo-réductifsgroupes quasi-réductifsmodèles de Néron

MSC classification

Primary: 14L15: Group schemes
Secondary: 14M15: Grassmannians, Schubert varieties, flag manifolds 20G25: Linear algebraic groups over local fields and their integers 20E42: Groups with a $BN$-pair; buildings
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 4 , July 2022 , pp. 1331 - 1362
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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