A guide to the reduction modulo p of Shimura varieties

By Michael Rapoport. 2002

206 citations recorded by the source corpus.

This is a report on results and methods in the reduction modulo p of Shimura varieties with parahoric level structure. In the first part, the local theory, we explain the concepts of parahoric subgroups, of the mu-admissible and mu-permissible subsets of the Iwahori-Weyl group, of the corresponding union of affine Deligne-Lusztig varieties and of local models. In the second part, the global theory, we use these concepts to formulate conjectures on the points in the reduction modulo p of Shimura varieties with parahoric level structure.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/369a58d173fdd0153abce6bc3df2d92094452d6f

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In Geometry and Topology

1. Xuhua He
2. E. Viehmann
3. Michael Rapoport
4. Thomas J. Haines
5. Xinwen Zhu
6. Georgios Pappas
7. Ulrich Goertz
8. U. Hartl

In Mathematical Physics

1. Xuhua He
2. Michael Rapoport
3. E. Viehmann
4. Georgios Pappas
5. Xinwen Zhu
6. Thomas J. Haines
7. Ulrich Goertz
8. U. Hartl

In Statistical and Nonlinear Physics

1. Xuhua He
2. Georgios Pappas
3. Thomas J. Haines
4. Xinwen Zhu
5. E. Viehmann
6. B. Smithling
7. Ulrich Goertz
8. Sean Rostami

Citations in the corpus

• Fully Hodge–Newton Decomposable Shimura Varieties (2016, background): “The {μ}-admissible set ([37], [43]) is defined by”
• The Newton stratification on deformations of local G-shtukas (2008, background): “5 Deformation theory of local G-shtukas 17 6 Rapoport-Zink spaces for local G-shtukas and affine Deligne-Lusztig varieties 22”
• Stratifications in the reduction of Shimura varieties (2015, methodology): “The background of these questions is addressed in the survey paper by Haines [10] and the survey paper of the second author [41], where early work on these problems is described.”
• Local models of Shimura varieties, I. Geometry and combinatorics (2010, methodology): “Because of this, the conjecture may in some sense be regarded as a version for arbitrary groups of the conjecture in [84] that Adm({μ}) = Perm({μ}) for minuscule cocharacters in split groups; see Remark 4.”
• The dimension of some affine Deligne–Lusztig varieties (2006, unknown): “Rapoport conjectured this in [7], Conjecture 5.”
• Local models in the ramified case. III Unitary groups (2007, methodology): “Affine Weyl groups We start by recalling some facts on affine Weyl groups [16,28].”