Related papers: On the flatness of models of certain Shimura varie…

Let p>2 be a rational prime, k be a perfect field of characteristic p and K be a finite totally ramified extension of the fractional field of the Witt ring of k. Let G and H be finite flat commutative group schemes killed by p over O_K and…

Let O_K be a discrete valuation ring of mixed characteristics (0,p), with residue field k. Using work of Sekiguchi and Suwa, we construct some finite flat O_K-models of the group scheme \mu_{p^n,K} of p^n-th roots of unity, which we call…

We introduce a notion of stable spherical variety which includes the spherical varieties under a reductive group $G$ and their flat equivariant degenerations. Given any projective space $\bP$ where $G$ acts linearly, we construct a moduli…

We study the basic locus of Shimura varieties associated to the group of spinor similitudes of a quadratic space over $\mathbb{Q}$ with level structure given by the stabilizer of a vertex lattice. We give a description of the underlying…

We prove a conjecture of Pappas and Rapoport for all Shimura varieties of abelian type with parahoric level structure when $p>3$ by showing that the Kisin-Pappas-Zhou integral models of Shimura varieties of abelian type are canonical. In…

This is a revised version of a part of the author's preprint "On p-adic uniformization of fake projective planes" (preprint, Max-Planck-Institut fuer Mathematik, 1998 (121)). In this paper we construct explicitly a Shimura surface of…

We develop a theory of $p$-adic automorphic forms on unitary groups that allows $p$-adic interpolation in families and holds for all primes $p$ that do not ramify in the reflex field $E$ of the associated unitary Shimura variety. If the…

Borrowing a reduction principle to a recent preprint of G. Faltings (toroidal resolution of some matrix singularities, 1999), we use Lafforgue's compactification of PGL_r^{N+1}/PGL_r to construct a canonical log-smooth toroidal resolution…

We prove under certain assumptions a formula for the cohomology of PEL-type Rapoport--Zink spaces that "averages" over the Kottwitz set. Our formula generalizes that of Shin's beyond the EL-type case and is proven by combining Mantovan's…

In this paper we study the geometry of good reductions of Shimura varieties of abelian type. More precisely, we construct the Newton stratification, Ekedahl-Oort stratification, and central leaves on the special fiber of a Shimura variety…

We investigate the relation between partial silting modules, Gabriel topologies, and ring epimorphisms, with a particular emphasis on commutative rings. We show that a ring epimorphism of commutative rings is flat if and only if it is a…

We construct regular integral canonical models for Shimura varieties attached to Spin groups at (possibly ramified) odd primes. We exhibit these models as schemes of 'relative PEL type' over integral canonical models of larger Spin Shimura…

The Hecke orbit conjecture asserts that every prime-to-$p$ Hecke orbit in a Shimura variety is dense in the central leaf containing it. In this paper, we prove the conjecture for certain irreducible components of Newton strata in Shimura…

We 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. We then prove that in Hodge type cases and…

We construct integral models of Shimura varieties of abelian type with parahoric level structure over odd primes. These models are \'etale locally isomorphic to corresponding local models.

The paper is a continuation of the paper of Kudla-Rapoport-Zink on $p$-adic uniformization of Shimura curves associated to a group of binary unitary similitudes. Here we consider two variants: first, the RSZ variant, for which we can allow…

We construct relative PEL type embeddings in mixed characteristic (0,2) between hermitian orthogonal Shimura varieties of PEL type. We use this to prove the existence of integral canonical models in unramified mixed characteristic (0,2) of…

In this article we develop the theory of local models for the moduli stacks of global $G$-shtukas, the function field analogs for Shimura varieties. Here $G$ is a smooth affine group scheme over a smooth projective curve. As the first…

We determine the type of the zeta functions and the range of the dimensions of the moduli spaces of finite flat models of two-dimensional local Galois representations over finite fields. This gives a generalization of Raynaud's theorem on…

Let $F$ be a totally real field in which a prime number $p>2$ is inert. We continue the study of the (generalized) Goren--Oort strata on quaternionic Shimura varieties over finite extensions of $\mathbb F_p$. We prove that, when the…