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On the arithmetic moduli schemes of PEL Shimura varieties

Georgios Pappas
- 01 Jul 2000 - 
- Vol. 9, Iss: 3, pp 577-605
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This article is published in Journal of Algebraic Geometry.The article was published on 2000-07-01 and is currently open access. It has received 94 citations till now.

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A guide to the reduction modulo p of Shimura varieties

Michael Rapoport
- 02 May 2002 - 
TL;DR: In this article, a report on results and methods in the reduction modulo p of Shimura varieties with parahoric level structure is given. But the results are restricted to the case where the subgroups of the Iwahori-Weyl group and the corresponding union of affine Deligne-Lusztig varieties are considered.
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Local models of Shimura varieties and a conjecture of Kottwitz

Georgios Pappas, +1 more
- 01 Oct 2013 - 
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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Introduction to Shimura Varieties with Bad Reduction of Parahoric Type

Thomas J. Haines
- 24 Sep 2004 - 
TL;DR: In this paper, a survey article explains the construction of Rapoport-Zink local models and their use in understanding various questions relating to the singularities in the reduction modulo p of certain Shimura varieties with parahoric level structure at p.
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Integral canonical models for Spin Shimura varieties

Keerthi Madapusi Pera
- 01 Apr 2016 - 
TL;DR: In this paper, the authors construct regular integral canonical models for Shimura varieties attached to Spin and orthogonal groups at (possibly ramified) primes, and show that the classical Kuga-Satake construction extends over the integral models.
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Local models in the ramified case I. The EL-case

Georgios Pappas, +1 more
- 18 Jul 2002 - 
TL;DR: In this paper, the flatness conjecture of Rapoport-Zink on local models fails in the presence of ramification and that in that case one has to modify their definition.