Related papers: Shimura Varieties and Moduli

We formulate an analogue of the archimedean motivic action conjecture of Prasanna--Venkatesh for irregular cohomological automorphic forms on Shimura varieties, which appear on multiple degrees of coherent cohomology of Shimura varieties.…

Given a closed immersion between arbitrary smooth complex projective varieties, we prove that the two operations: (1) taking the moduli space of stable sheaves, and (2) taking the deformation to the normal cone, commute in a precise sense.…

The goal of this paper is to prove a formula expressing the modular height of a unitary Shimura variety over a CM number field in terms of the logarithm derivative of the Hecke L-function associated with the CM extension. In a more specific…

We define variants of PEL type of the Shimura varieties that appear in the context of the Arithmetic Gan-Gross-Prasad conjecture. We formulate for them a version of the AGGP conjecture. We also construct (global and semi-global) integral…

Moduli spaces of quadratic differentials with prescribed singularities are not necessarily connected. We describe here all cases when they have a special hyperelliptic connected component. We announce the general classification theorem: up…

Modular flavor symmetries refers to scenarios in which fermion masses respect modular symmetries. Such scenarios have been studied in the bottom-up approach and have an explicit realization in string theory. They rely on the remarkable…

We prove the existence of integral canonical models of unitary Shimura varieties in arbitrary unramified mixed characteristic. Errata to [Va1] are also included.

We define a relation that describes the ternary commutator for congruence modular varieties. Properties of this relation are used to investigate the theory of the higher commutator for congruence modular varieties.

Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.

The Hikita conjecture relates the coordinate ring of a conical symplectic singularity to the cohomology ring of a symplectic resolution of the dual conical symplectic singularity. We formulate a quantum version of this conjecture, which…

We construct explicit generating series of arithmetic extensions of Kudla's special divisors on integral models of unitary Shimura varieties over CM fields with arbitrary split levels and prove that they are modular forms valued in the…

We establish a correspondence between vector-valued modular forms with respect to a symmetric tensor representation and quasimodular forms. This is carried out by first obtaining an explicit isomorphism between the space of vector-valued…

We describe the quantum cohomology rings of a class of toric varieties. The description includes, in addition to the (already known) ring presentations, the (new) analogues for toric varieties of the sorts of quantum Giambelli formulas…

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.

We give an explicit version of Shimura's reciprocity law for singular values of Siegel modular functions. We use this to construct the first examples of class invariants of quartic CM fields that are smaller than Igusa invariants. Our…

We express the cohomology of the basic stratum of some unitary Shimura varieties associated to division algebras in terms of automorphic representations of the group in the Shimura datum.

We define a new invariant of finitely generated representations of a finite group, with coefficients in a commutative noetherian ring. This invariant uses group cohomology and takes values in the singularity category of the coefficient…

We define relative support varieties with respect to some fixed module over a finite dimensional algebra. These varieties share many of the standard properties of classical support varieties. Moreover, when introducing finite generation…

We classify curves in the moduli space of curves that are both Shimura- and Teichmueller curves: Except for the moduli space of genus one curves there is only a single such curve. We start with a Hodge-theoretic description of Shimura…

We prove the Kudla--Rapoport conjecture for Kr\"amer models of unitary Rapoport--Zink spaces at ramified places. It is a precise identity between arithmetic intersection numbers of special cycles on Kr\"amer models and modified derived…