Good and semi-stable reductions of Shimura varieties

Xuhua He; Georgios Pappas; Michael Rapoport

doi:10.5802/jep.123

Good and semi-stable reductions of Shimura varieties
[Bonne réduction et réduction semi-stable de variétés de Shimura]

Xuhua He ¹ ; Georgios Pappas ² ; Michael Rapoport ³

¹ Department of Mathematics, University of Maryland College Park, MD 20742, USA
² Dept. of Mathematics, Michigan State University E. Lansing, MI 48824, USA
³ Mathematisches Institut der Universität Bonn Endenicher Allee 60, 53115 Bonn, Germany and Department of Mathematics, University of Maryland College Park, MD 20742, USA

Journal de l’École polytechnique — Mathématiques, Tome 7 (2020), pp. 497-571.

Résumé
Abstract

Nous étudions des variantes des modèles locaux introduits par le deuxième auteur et Zhu, et les modèles intégraux correspondants des variétés de Shimura de type abélien. Nous déterminons tous les cas de bonne réduction, resp. de réduction semi-stable, sous des hypothèses de ramification modérée.

We study variants of the local models constructed by the second author and Zhu and consider corresponding integral models of Shimura varieties of abelian type. We determine all cases of good, resp. of semi-stable, reduction under tame ramification hypotheses.

Reçu le : 2018-10-11
Accepté le : 2020-03-06
Publié le : 2020-03-25

DOI : 10.5802/jep.123

Classification : 11G18, 14G35
Keywords: Shimura varieties, local models, Rapoport-Zink spaces, Schubert varieties
Mot clés : Variétés de Shimura, modèles locaux, espaces de Rapoport-Zink, variétés de Schubert

Affiliations des auteurs :

Xuhua He ¹ ; Georgios Pappas ² ; Michael Rapoport ³

¹ Department of Mathematics, University of Maryland College Park, MD 20742, USA
² Dept. of Mathematics, Michigan State University E. Lansing, MI 48824, USA
³ Mathematisches Institut der Universität Bonn Endenicher Allee 60, 53115 Bonn, Germany and Department of Mathematics, University of Maryland College Park, MD 20742, USA

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Xuhua He and Georgios Pappas and Michael Rapoport},
     title = {Good and semi-stable reductions of {Shimura~varieties}},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
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Xuhua He; Georgios Pappas; Michael Rapoport. Good and semi-stable reductions of Shimura varieties. Journal de l’École polytechnique — Mathématiques, Tome 7 (2020), pp. 497-571. doi : 10.5802/jep.123. https://jep.centre-mersenne.org/articles/10.5802/jep.123/

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