A guide to the reduction modulo p of Shimura varieties

Abstract

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.

AMS-TeX, 40 pages

References in corpus (1)

• Alcoves et p-rang des variétés abéliennes

Cited by in corpus (63)

• Ekedahl-Oort and Newton strata for Shimura varieties of PEL type
• Towards a theory of local Shimura varieties
• Rapoport-Zink spaces for spinor groups
• An introduction to affine Grassmannians and the geometric Satake equivalence
• Introduction to Shimura varieties with bad reduction of parahoric type
• The Newton stratification on deformations of local G-shtukas
• On parahoric subgroups
• Local models of Shimura varieties, I. Geometry and combinatorics
• Basic loci in Shimura varieties of Coxeter type
• Fully Hodge-Newton decomposable Shimura varieties
• The global structure of moduli spaces of polarized p-divisible groups
• Twisted orbital integrals and irreducible components of affine Deligne-Lusztig varieties
• Affine Grassmannians and the geometric Satake in mixed characteristic
• The supersingular locus of unitary Shimura varieties with exotic good reduction
• Rapoport-Zink spaces of Hodge type
• The Discriminant of an Algebraic Torus
• $P$-alcoves and nonemptiness of affine Deligne-Lusztig varieties
• On the Hodge-Newton decomposition for split groups
• Kottwitz-Rapoport conjecture on unions of affine Deligne-Lusztig varieties
• On the coherence conjecture of Pappas and Rapoport
• Hecke algebras and $p$-adic groups
• Integral models of Shimura varieties with parahoric level structure
• Moduli spaces of p-divisible groups
• EKOR strata for Shimura varieties with parahoric level structure
• The dimension of affine Deligne-Lusztig varieties in the affine Grassmannian of unramified groups
• Affine Bruhat order and Demazure products
• Vertexwise criteria for admissibility of alcoves
• Note on affine Deligne-Lusztig varieties
• Dimensions of Newton strata in the adjoint quotient of reductive groups
• Closure of Steinberg fibers and affine Deligne-Lusztig varieties
• On the p-adic cohomology of the Lubin-Tate tower
• Stratifications of affine Deligne-Lusztig varieties
• Cordial elements and dimensions of affine Deligne-Lusztig varieties
• On integral models of Shimura varieties
• Twisted loop groups and their affine flag varieties
• Central leaves on Shimura varieties with parahoric reduction
• Good and semi-stable reductions of Shimura varieties
• Admissibility and permissibility for minuscule cocharacters in orthogonal groups
• On a decomposition of $p$-adic Coxeter orbits
• Semi-modules and irreducible components of affine Deligne-Lusztig varieties
• Equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic
• Geometric and homological properties of affine Deligne-Lusztig varieties
• Topological flatness of orthogonal local models in the split, even case. I
• Local models of Shimura varieties and a conjecture of Kottwitz
• Dimensions of some affine Deligne-Lusztig varieties
• On central leaves of Hodge-type Shimura varieties with parahoric level structure
• Connectedness of affine Deligne-Lusztig varieties for unramified groups
• Stratifications in the reduction of Shimura varieties
• On the $\mu$-admissible set in the extended affine Weyl groups of $E_6$ and $E_7$
• Combinatorics of the basic stratum
• On the cohomology of compact unitary group Shimura varieties at ramified split places
• Notes on partial conjugation
• Galois gerbs and Lefschetz number formula for Shimura varieties of Hodge type
• Connected components of closed affine Deligne-Lusztig varieties
• Local Models in the ramified case. III. Unitary groups
• A converse to Mazur's inequality for split classical groups
• Existence de F-cristaux avec structures supplementaires
• On the slope stratification of certain Shimura varieties
• Dimension formula of the affine Deligne-Lusztig variety $X(\mu ,b)$
• Formulas for the dimensions of some affine Deligne-Lusztig Varieties
• EKOR strata on Shimura varieties with parahoric reduction
• $l$-adic étale cohomology of Shimura varieties of Hodge type with non-trivial coefficients
• The dimension of some affine Deligne-Lusztig varieties