Rapoport-Zink spaces for spinor groups

Abstract

We develop a theory of Hodge type Rapoport-Zink formal schemes, which uniformize certain formal completions of the canonical integral models of Shimura varieties of Hodge type at primes of good reduction. We then apply the general theory to the special case of Shimura varieties associated with groups of spinor similitudes, and, in the basic case, determine explicitly the reduced scheme underlying the Rapoport-Zink formal scheme.

66pp, final version, to appear in Compositio Math

References in corpus (14)

• A guide to the reduction modulo p of Shimura varieties
• Towards a theory of local Shimura varieties
• Connected components of affine Deligne-Lusztig varieties in mixed characteristic
• Integral canonical models for Spin Shimura varieties
• The μ-ordinary locus for Shimura varieties of Hodge type
• On the supersingular locus of the GU(2,2) Shimura variety
• Basic loci in Shimura varieties of Coxeter type
• Affine Grassmannians and the geometric Satake in mixed characteristic
• Rapoport-Zink spaces of Hodge type
• Stratifications and foliations for good reductions of Shimura varieties of Hodge type
• Integral models of Shimura varieties with parahoric level structure
• The supersingular locus of the Shimura variety for GU(1,n-1) over a ramified prime
• Ekedahl-Oort strata for good reductions of Shimura varieties of Hodge type
• Affine Deligne-Lusztig varieties and the action of J

Cited by in corpus (27)

• Fully Hodge-Newton decomposable Shimura varieties
• Twisted orbital integrals and irreducible components of affine Deligne-Lusztig varieties
• Picard ranks of K3 surfaces over function fields and the Hecke orbit conjecture
• Affine Grassmannians and the geometric Satake in mixed characteristic
• Fine Deligne-Lusztig varieties and Arithmetic Fundamental Lemmas
• Stratifications and foliations for good reductions of Shimura varieties of Hodge type
• On some generalized Rapoport-Zink spaces
• Arithmetic intersection on GSpin Rapoport-Zink spaces
• Arithmetic degrees of special cycles and derivatives of Siegel Eisenstein series
• On the Newton stratification in the good reduction of Shimura varieties
• On the Bruhat-Tits stratification of a quaternionic unitary Shimura variety
• On Irreducible Symplectic Varieties of ${K3}^{[n]}$-type in Positive Characteristic
• The generic fiber of moduli spaces of bounded local $G$-shtukas
• On integral local Shimura varieties
• Eichler-Shimura Relations for Shimura Varieties of Hodge Type
• On supersingular loci of Shimura varieties for quaternionic unitary groups of degree $2$
• On quaternionic unitary Rapoport-Zink spaces with parahoric level structures
• The ${\mathrm{GL}}_4$ Rapoport-Zink Space
• Notes on Rapoport--Zink spaces of Hodge type with parahoric level structure
• Construction of a Rapoport-Zink space for $\mathrm{GU}(1,1)$ in the ramified $2$-adic case
• On the supersingular locus of the Shimura variety for $\mathrm{GU}(2,2)$ over a ramified prime
• A Tannakian framework for $G$-displays and Rapoport-Zink spaces
• Hecke eigensystems of automorphic forms (mod $p$) of Hodge type and algebraic modular forms
• On central leaves of Hodge-type Shimura varieties with parahoric level structure
• Rapoport--Zink spaces for spinor groups with special maximal parahoric level structure
• On the Bruhat-Tits stratification for GU(2,2) type Rapoport-Zink space: unramified case
• $l$-adic étale cohomology of Shimura varieties of Hodge type with non-trivial coefficients