Related papers: Special cycles on unitary Shimura curves at ramifi…
We study the local behavior of special cycles on Shimura varieties for $\mathbf{U}(2, 1) \times \mathbf{U}(1, 1)$ in the setting of the Gan-Gross-Prasad conjectures at primes $\tau$ of the totally real field of definition of the unitary…
In this article, we study local models associated to certain Shimura varieties. In particular, we present a resoultion of their singularities. As a consequence, we are able to determine the alternating semisimple trace of the geometric…
We prove $p$-adic uniformization for Shimura curves attached to the group of unitary similitudes of certain binary skew hermitian spaces $V$ with respect to an arbitrary CM field $K$ with maximal totally real subfield $F$. For a place $v|p$…
In this largely expository note, we explain some recent progress on new cycles on Shimura varieties and Rapoport-Zink spaces, (twisted) arithmetic fundamental lemma, and arithmetic analogs of relative Langlands program. We explain related…
We consider Shimura varieties associated to a unitary group of signature $(n-1, 1)$. For these varieties, we construct $p$-adic integral models over odd primes $p$ which ramify in the imaginary quadratic field with level subgroup at $p$…
In this paper, we formulate conjectural formulas for the arithmetic intersection numbers of special cycles on unitary Shimura varieties with minuscule parahoric level structure. Also, we prove that these conjectures are compatible with all…
In this paper, we reformulate conjectural formulas for the arithmetic intersection numbers of special cycles on unitary Shimura varieties with minuscule parahoric level structure in terms of weighted counting of lattices containing special…
In this note we study the supersingular locus of the GU(2,2) Shimura variety modulo a prime which is unramified in the imaginary quadratic extension. The supersingular locus of this Shimura variety can be related to the basic Rapoport-Zink…
In this article, we improve our main results from \emph{Chow groups and $L$-derivatives of automorphic motives for unitary groups} in two direction: First, we allow ramified places in the CM extension $E/F$ at which we consider…
We prove the geometrical Satake isomorphism for a reductive group defined over F=k((t)), and split over a tamely ramified extension. As an application, we give a description of the nearby cycles on certain Shimura varieties via the…
We consider arithmetic analogs of the relative Langlands program and applications of new non-reductive geometry. Firstly, we introduce mirabolic special cycles, which produce special cycles on many Hodge type Rapoport-Zink spaces via…
We describe the structure of the supersingular locus of a Shimura variety for a quaternionic unitary similitude group of degree $2$ over a ramified odd prime $p$ if the level at $p$ is given by a special maximal compact open subgroup. More…
We consider Shimura varieties associated to a unitary group of signature $(2,n-2)$. We give regular $p$-adic integral models for these varieties over odd primes $p$ which ramify in the imaginary quadratic field with level subgroup at $p$…
We consider two families of arithmetic divisors defined on integral models of Shimura curves. The first was studied by Kudla, Rapoport and Yang, who proved that if one assembles these divisors in a formal generating series, one obtains the…
We study unramified sections of the fundamental group sequence of smooth projective curves of genus $\geq 2$ over $p$-adic fields together with an integral model. We are particularly interested in the induced specialized sections of the…
Let V be a rational quadratic space of signature (m,2). A conjecture of Kudla relates the arithmetic degrees of top degree special cycles on an integral model of a Shimura variety associated with SO(V) to the coefficients of the central…
Let $F$ be a totally real field in which a fixed prime $p$ is inert, and let $E$ be a CM extension of $F$ in which $p$ splits. We fix two positive integers $r,s \in \mathbb N$. We investigate the Tate conjecture on the special fiber of…
In this paper, we study the basic locus in the fiber at $p$ of a certain unitary Shimura variety with a certain parahoric level structure. The basic locus $\widehat{\mathcal{M}^{ss}}$ is uniformized by a formal scheme $\mathcal{N}$ which is…
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…
The integral model of a $\mathrm{GU}(n-1,1)$ Shimura variety carries a universal abelian scheme over it, and the dual top exterior power of its Lie algebra carries a natural hermitian metric. We express the arithmetic volume of this…