Related papers: Integral models of Shimura varieties with parahori…
We express the Frobenius-Hecke traces on the compactly supported cohomology of a Shimura variety of abelian type in terms of elliptic parts of stable Arthur-Selberg trace formulas for the endoscopic groups. This confirms predictions of…
We prove that central leaves, Igusa varieties, Newton strata, Kottwitz-Rapoport Strata, Ekedahl-Kottwitz-Oort-Rapoport strata on the special fiber of a Kisin-Pappas integral model of a Hodge-type Shimura variety with connected parahoric…
We construct flat integral moduli schemes of PEL type D and the corresponding flat orthogonal Rapoport--Zink spaces with parahoric level structure over a $p$-adic integer ring. The construction relies on proving a conjecture of…
We prove the existence of weak integral canonical models of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic $(0,p)$. As a first application we solve a conjecture of Langlands for Shimura varieties of Hodge type.…
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…
We construct integral models and special affinoids of suitable tubular neighborhoods of local Shimura varieties at depth-zero. We show that the reductions of the special affinoids over suitable tamely ramified extensions are realized as…
We provide a moduli description of the ramified unitary local model of signature $(n-1,1)$ with arbitrary parahoric level structure, assuming the residue field has characteristic not equal to $2$, thereby confirming a conjecture of…
This is a largely expository article based on our previous work on arithmetic diagonal cycles on unitary Shimura varieties. We define a class of Shimura varieties closely related to unitary groups which represent a moduli problem of abelian…
We study the mod $p$-points of the Kisin--Pappas integral models of Shimura varieties of Hodge type with parahoric level. We show that if the group is quasi-split, then every isogeny class contains the reduction of a CM point, proving a…
We use the idea of splitting models to define and study a semi-stable model for unitary Shimura varieties of signature $(n-1,1)$ with maximal parahoric level structure at ramified primes. In this case, the ``naive'' splitting model defined…
For any Shimura variety of Hodge type with hyperspecial level at a prime $p$ and automorphic lisse sheaf on it, we prove a formula, conjectured by Kottwitz \cite{Kottwitz90}, for the Lefschetz numbers of Frobenius-twisted Hecke…
In this article, we prove results about the cohomology of compact unitary group Shimura varieties at split places. In nonendoscopic cases, we are able to give a full description of the cohomology, after restricting to integral Hecke…
We establish a representability criterion of $v$-sheaf theoretic modifications of formal schemes and apply this criterion to moduli spaces of parahoric level structures on local shtukas. In the proof, we introduce nice classes of…
We prove the test function conjecture of Kottwitz and the first named author for local models of Shimura varieties with parahoric level structure, and their analogues in equal characteristic.
This paper proves that the nearby cycles complexes on a certain family of PEL local models are central with respect to the convolution product of sheaves on the corresponding affine flag varieties. As a corollary, the semisimple trace…
We study the Piatetski-Shapiro construction, which takes a totally real field F and a Shimura datum (G,X) and produces a new Shimura datum (H,Y). If F is Galois, then the Galois group Gamma of F acts on (H,Y), and we show that the…
We define and construct integral canonical models for automorphic vector bundles over Shimura varieties of abelian type. More precisely, we first build on Kisin's work to construct integral canonical models over rings of integers of number…
In this paper, we compute the cohomology sheaves of the $\ell$-adic nearby cycles on the local model of the PEL $\mathrm{GU}(n-1,1)$ Shimura variety over a ramified prime, with level given by the stabilizer of a self-dual lattice. This…
We show that special cycles generate a large part of the cohomology of locally symmetric spaces associated to orthogonal groups. We prove in particular that classes of totally geodesic submanifolds generate the cohomology groups of degree…
We determine the detailed structure of parabolic subgroups of orthogonal groups over $\mathbb{Z}$, and deduce the precise form of canonical boundary components in toroidal compactifications of orthogonal Shimura varieties.