Related papers: Local models of Shimura varieties, I. Geometry and…
We provide an axiomatic approach to the theory of local tangent cones of regular sub-Riemannian manifolds and the differentiability of mappings between such spaces. This axiomatic approach relies on a notion of a dilation structure which is…
Let $\overline{\mathtt{X}}_\lambda$ be the closure of the $\mathtt{I}$-orbit $\mathtt{X}_\lambda$ in the affine Grassmanian $\mathtt{Gr}$ of a simple algebraic group $G$ of adjoint type, where $\mathtt{I}$ is the Iwahori group and $\lambda$…
This is the last in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global conformal invariants''; these are defined to be conformally invariant integrals of geometric scalars.…
We describe several explicit examples of simple abelian surfaces over real quadratic fields with real multiplication and everywhere good reduction. These examples provide evidence for the Eichler-Shimura conjecture for Hilbert modular forms…
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…
A survey of problems, conjectures, and theorems about quasi-isometric classification and rigidity for finitely generated solvable groups.
We define linear degenerations of Schubert varieties via a special class of quiver Grassmannians. To do so, we restrict our study to an appropriate subvariety in the variety of representations of the considered quiver and describe a base…
In this article we describe relations of the topology of closed 1-forms to the group theoretic invariants of Bieri-Neumann-Strebel-Renz. Starting with a survey, we extend these Sigma invariants to finite CW- complexes and show that many…
The authors developed in a recent paper natural dualities for finitely generated quasivarieties of Sugihara algebras. They thereby identified the admissibility algebras for these quasivarieties which, via the Test Spaces Method devised by…
Given a morphism $f: X \rightarrow S$ of complex algebraic varieties and a constructible sheaf $\mathcal{G}$ on $X$, we compute the local monodromy of $Rf_*(\mathcal{G})$ and $Rf_!(\mathcal{G})$ in terms of the local monodromy of…
We prove that the generating series of special divisors in toroidal compactifications of orthogonal Shimura varieties is a mixed mock modular form. More precisely, we find an explicit completion using theta series associated to rays in the…
We axiomatize the algebraic properties of toroidal compactifications of (mixed) Shimura varieties and their automorphic vector bundles. A notion of generalized automorphic sheaf is proposed which includes sheaves of (meromorphic) sections…
Cluster varieties are geometric objects that have recently found applications in several areas of mathematics and mathematical physics. This thesis studies the geometry of a large class of cluster varieties associated to compact oriented…
We construct a family of special cycle classes on the regular integral model of an orthogonal Shimura variety, and show that these cycle classes appear as Fourier coefficients of a Siegel modular form. Passing to the generic fiber of the…
We construct Eigenvarieties for PEL Shimura varieties which interpolate cuspidal, finite slope automorphic forms for PEL Shimura varieties appearing as global sections of (coherent) automorphic sheaves, under the hypothesis that the primes…
The absolute sets of local systems on a smooth complex algebraic variety are the subject of a conjecture of N. Budur and B. Wang based on an analogy with special subvarieties of Shimura varieties. An absolute set should be the…
We prove the local Kudla--Rapoport conjecture, which is a precise identity between the arithmetic intersection numbers of special cycles on unitary Rapoport--Zink spaces and the derivatives of local representation densities of hermitian…
In this paper, we give a notion of the potentially good reduction locus of a Shimura variety. It consists of the points which should be related with motives having potentially good reductions in some sense. We show the existence of such…
Geometric/arithmetic theta correspondences provide correspondences between automorphic forms and cohomology classes/algebraic cycles on Shimura varieties. We give an introduction focusing on the example of unitary groups and highlight…
In this paper we show that every locally finite quasivariety of MV-algebras is finitely generated and finitely based. To see this result we study critical MV-algebras. We also give axiomatizations of some of these quasivarieties.