Twisted loop groups and their affine flag varieties
Georgios Pappas,Michael Rapoport +1 more
TLDR
In this article, a theory of affine flag varieties and Schubert varieties for reductive groups over a Laurent power series local field k((t)) with k a perfect field was developed.About:
This article is published in Advances in Mathematics.The article was published on 2008-09-10 and is currently open access. It has received 271 citations till now. The article focuses on the topics: Flag (geometry) & Shimura variety.read more
Citations
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Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale
TL;DR: For any reductive group G over a global function field, the authors used the cohomology of G-shtukas with multiple modifications and the geometric Satake equivalence to prove the global Langlands correspondence for G in the direction from automorphic to Galois.
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Local models of Shimura varieties and a conjecture of Kottwitz
Georgios Pappas,Xinwen Zhu +1 more
TL;DR: In this paper, a group theoretic definition of local models of Grassmannian degenerations of Shimura varieties has been given, which are obtained by extending constructions of Beilinson, Drinfeld, Gaitsgory and the second-named author to mixed characteristics and to the case of general reductive groups.
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Projectivity of the Witt vector affine Grassmannian
Bhargav Bhatt,Peter Scholze +1 more
TL;DR: In this paper, it was shown that the Witt vector affine Grassmannian, which parametrizes W(k)-lattices in a perfect field k of characteristic p, is representable by an ind-(perfect scheme) over k. This improves on previous results of Zhu by constructing a natural ample line bundle.
Posted Content
Affine Grassmannians and the geometric Satake in mixed characteristic
TL;DR: In this article, the authors prove the representability of affine Grassmannians and establish the geometric Satake correspondence in mixed characteristic, and also give an application of their theory to the study of Rapoport-Zink spaces.
Journal ArticleDOI
Affine Grassmannians and the geometric Satake in mixed characteristic
TL;DR: In this paper, the authors prove the representability of affine Grassmannians and establish the geometric Satake equivalence in mixed characteristic, and also give an application of their theory to the study of Rapoport Zink spaces.
References
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Book
Infinite Dimensional Lie Algebras
TL;DR: The invariant bilinear form and the generalized casimir operator are integral representations of Kac-Moody algebras and the weyl group as mentioned in this paper, as well as a classification of generalized cartan matrices.
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Éléments de géométrie algébrique : IV. Étude locale des schémas et des morphismes de schémas, Troisième partie
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Hodge Cycles, Motives, and Shimura Varieties
TL;DR: In this article, Langlands's construction of the Taniyama Group is described, as well as the construction of a Taniya Group for Hodge Cycles on Abelian Varieties.
Journal ArticleDOI
Regular elements of semi-simple algebraic groups
TL;DR: In this paper, the authors present a legal opinion on the use of commercial or impression systématiques in the context of the IHES agreement with the conditions générales d'utilisation.