Related papers: Local models for ramified unitary groups

We define the class of rigid Frobenius algebras in a (non-semisimple) modular category and prove that their categories of local modules are, again, modular. This generalizes previous work of A. Kirillov, Jr. and V. Ostrik [Adv. Math. 171…

We formulate a detailed conjectural Eichler-Shimura type formula for the cohomology of local systems on a Picard modular surface associated to the group of unitary similitudes $\mathrm{GU}(2,1,\mathbb{Q}(\sqrt{-3}))$. The formula is based…

We study a Shimura variety attached to a unitary similitude group of a skew-Hermitian form over a totally indefinite quaternion algebra over a totally real number field. We give a necessary and sufficient condition for the existence of…

We survey recent results on a conjecture of Kudla regarding the modularity of generating series of special cycle classes in toroidal compactifications of orthogonal and unitary Shimura varieties. Along the way, we formulate several…

The goal of this paper is to clarify the connection between certain structures from the theory of totally nonnegative Grassmannians, quiver Grassmannians for cyclic quivers and the theory of local models of Shimura varieties. More…

We study Shimura (special) subvarieties in the moduli space $A_{p,D}$ of complex abelian varieties of dimension $p$ and polarization type $D$. These subvarieties arise from families of covers compatible with a fixed group action on the base…

For a smooth morphism $f: X \longrightarrow \Sigma$ of real analytic manifolds and an $\mathbb{R}$-constructible sheaf $F$ on $X$ satisfying some condition, we define a family of Lagrangian cycles parameterized by $\Sigma$ that we call the…

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…

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 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.

Local models of Shimura varieties in type A can be realized inside products of Grassmannians via certain linear algebraic conditions. Laumon suggested a generalization which can be identified with a family over a line whose general fibers…

We define and study new filtrations called of stratification of a perverse sheaf on a scheme; beside the cases of the weight or monodromy filtrations, these filtrations are available whatever are the ring of coefficients. We illustrate…

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…

Let G be a unitary group over a totally real field, and X a Shimura variety for G. For certain primes p of good reduction for X, we construct cycles on the characteristic p fiber of X. These cycles are defined as the loci on which the…

We study the Jordan-Hoelder series for nearby cycles on certain Shimura varieties and Rapoport-Zink local models, and on finite-dimensional pieces of Beilinson's deformation of the affine Grassmannian to the affine flag variety (and their…

In this paper, we use a group-theoretic approach to give a concrete description of the geometric structure of the supersingular locus of unitary Shimura varieties with exotic good reduction. This approach also is a more uniform way to prove…

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 construct (cohomological) correspondences between mod $p$ fibers of different Shimura varieties and describe the fibers of these correspondences by studying irreducible components of affine Deligne-Lusztig varieties. In particular, in…

We study $p$-adic integral models of certain PEL Shimura varieties with level subgroup at $p$ related to the $\Gamma_1(p)$-level subgroup in the case of modular curves. We will consider two cases: the case of Shimura varieties associated…

In this paper, we investigate a general method to establish tame and norm relations for special cycles in Shimura varieties, using unitary cycles in odd orthogonal Shimura varieties as a guiding example.