Related papers: On the geometry of splitting models

We study $p$-adic properties of the coherent cohomology of some automorphic sheaves on the Hilbert modular variety $X$ for a totally real field $F$ in the case where the prime $p$ is totally split in $F$. More precisely, we develop higher…

We give an expository overview over recent results on the global structure and geometry of the Newton stratification of the reduction modulo p of Shimura varieties of Hodge type with hyperspecial level structure. More precisely, we discuss…

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 prove an analogue of the Madsen-Weiss theorem for high dimensional manifolds. For example, we explicitly describe the ring of characteristic classes of smooth fibre bundles whose fibres are connected sums of g copies of S^n x S^n, in the…

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 study the \'etale cohomology of Hilbert modular varieties, building on the methods introduced for unitary Shimura varieties in [CS17, CS19]. We obtain the analogous vanishing theorem: in the "generic" case, the cohomology with torsion…

We establish normal form theorems for a large class of singular flat connections on complex manifolds, including connections with logarithmic poles along weighted homogeneous Saito free divisors. As a result, we show that the moduli spaces…

Let $(\mathsf{G},\mathsf{X})$ be a Shimura datum of Hodge type. Let $p$ be an odd prime such that $\mathsf{G}_{\mathbb{Q}_p}$ splits after a tamely ramified extension and $p\nmid |\pi_1(\mathsf{G}^{\rm der})|$. Under some mild additional…

We give a construction of "integral local Shimura varieties" which are formal schemes that generalize the well-known integral models of the Drinfeld $p$-adic upper half spaces. The construction applies to all classical groups, at least for…

Local models are schemes defined in linear algebra terms that describe the 'etale local structure of integral models for Shimura varieties and other moduli spaces. We point out that the flatness conjecture of Rapoport-Zink on local models…

We prove an arithmetic Hilbert-Samuel type theorem for semi-positive singular hermitian line bundles of finite height. In particular, the theorem applies to the log-singular metrics of Burgos-Kramer-K\"uhn. Our theorem is thus suitable for…

We study truncated gauge-orbits through principal parts of irregular-singular connection germs, in the untwisted/unramified setting: for any connected complex reductive structure group $G$, in the general multilevel case. In particular, we…

We prove two formulas in the style of the Gross-Zagier theorem, relating derivatives of L-functions to arithmetic intersection pairings on a unitary Shimura variety. We also prove a special case of Colmez's conjecture on the Faltings…

We compute the level groups associated with mixed Shimura varieties that appear at the boundaries of compactifications of Shimura varieties and show that the boundaries of minimal compactifications of Pappas-Rapoport integral models are…

We use a variation of a classical construction of A. Hatcher to construct virtually all stable exotic smooth structures on compact smooth manifold bundles whose fibers have sufficiently large odd dimension (at least twice the base dimension…

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…

In this paper we show that certain Shimura varieties, uniformized by the product of complex unit balls, can be p-adically uniformized by the product (of equivariant coverings) of Drinfeld upper half-spaces. We also extend a p-adic…

We exhibit basic algebro-geometric results on the formal model of semi-infinite flag varieties and its Schubert varieties over an algebraically closed field $\mathbb K$ of characteristic $\neq 2$ from scratch. We show that the formal model…

We introduce a notion of Gieseker stability for coherent sheaves on tame Deligne-Mumford stacks with projective moduli scheme and some chosen generating sheaf on the stack in the sense of Olsson and Starr \cite{MR2007396}. We prove that…

Let M be the Shimura variety associated with the group of spinor similitudes of a rational quadratic space over of signature (n,2). We prove a conjecture of Bruinier-Kudla-Yang, relating the arithmetic intersection multiplicities of special…