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Good and semi-stable reductions of Shimura varieties

Xuhua He, +2 more
- Vol. 7, pp 497-571
TLDR
In this article, the authors study variants of the local models constructed by the second author and Zhu and consider corresponding integral models of Shimura varieties of abelian type and determine all cases of good, resp. of semi-stable, reduction under tame ramification hypotheses.
Abstract
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.

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Local models for ramified unitary groups

TL;DR: In this paper, local models associated to certain Shimura varieties are studied and a resoultion of their singularities is presented, which is able to determine the alternating semisimple trace of the geometric Frobenius on the sheaf of nearby cycles.
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EKOR strata for Shimura varieties with parahoric level structure

TL;DR: In this paper, the geometry of reduction modulo $p$ of the Kisin-Pappas integral models for certain Shimura varieties of abelian type with parahoric level structure is studied.
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Normality and Cohen-Macaulayness of parahoric local models

TL;DR: In this paper, the singularities of integral models of Shimura varieties and moduli stacks of shtukas with parahoric level structure were studied, and it was shown that the entire local model is normal with reduced special fiber and, if p>2, it is also Cohen-Macaulay.
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On integral models of Shimura varieties

TL;DR: In this article, the authors show how to characterize integral models of Shimura varieties over places of the reflex field where the level subgroup is parahoric by formulating a definition of a "canonical" integral model.
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On Shimura varieties for unitary groups

TL;DR: In this paper, a class of Shimura varieties closely related to unitary groups which represent a moduli problem of abelian varieties with additional structure, and which admit interesting algebraic cycles is defined.
References
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Journal ArticleDOI

Representations of Coxeter Groups and Hecke Algebras.

TL;DR: In this article, the problem of decomposing this space of functions into irreducible representations of a finite Chevalley group G(Fq) is equivalent to decomposing the regular representation o f ~ | | (12) of a Coxeter group.
Book

Lie groups and Lie algebras

TL;DR: Seligman as mentioned in this paper presents a rich and useful volume of material beyond the theory of Lie groups and algebras, ranging from the geometry of regular polytopes and paving problems to current work on finite simple groups having a (B,N)-pair structure, or "Tits systems".
Book

Kac-Moody Groups, their Flag Varieties and Representation Theory

Shrawan Kumar
TL;DR: In this article, Kac-Moody Lie Algebra Homology and Cohomology has been studied in the context of representation theory of kac-moody groups.
Journal ArticleDOI

On some bruhat decomposition and the structure of the hecke rings of p-Adic chevalley groups

TL;DR: In this article, 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.
Book

Period Spaces for p-divisible Groups

TL;DR: In this paper, the relation of "p"-adic period domains to moduli space of arbitrary reductive groups is investigated, and nonarchimedean uniformization theorems for general Shimura varieties are established.