Vertical Distribution Relations for Special Cycles on Unitary Shimura Varieties

Special Cycles on Unitary Shimura Varieties I. Unramified Local Theory

A relation between a generating series constructed from arithmetic cycles on an integral model of a Shimura curve and the derivative of a Siegel Eisenstein series of genus 2 was established by one of us in [9]. There, the hope is expressed that such a relation should hold in greater generality for integral models of Shimura varieties attached to orthogonal groups of signature (2, n − 2) for any...

Rankin-selberg L-functions and Cycles on Unitary Shimura Varieties

Modularity of Generating Functions of Special Cycles on Shimura Varieties

Modularity of Generating functions of Special Cycles on Shimura Varieties

Unitary Cycles on Shimura Curves and the Shimura Lift I

This paper concerns two families of divisors, which we call the ‘orthogonal’ and ‘unitary’ special cycles, defined on integral models of Shimura curves. The orthogonal family was studied extensively by Kudla-Rapoport-Yang, who showed that they are closely related to the Fourier coefficients of modular forms of weight 3/2, while the unitary divisors are analogues of cycles appearing in more rece...

P -adic Uniformization of Unitary Shimura Varieties

Introduction Let Γ ⊂ PGUd−1,1(R) 0 be a torsion-free cocompact lattice. Then Γ acts on the unit ball B ⊂ C by holomorphic automorphisms. The quotient Γ\B is a complex manifold, which has a unique structure of a complex projective variety XΓ (see [Sha, Ch. IX, §3]). Shimura had proved that when Γ is an arithmetic congruence subgroup, XΓ has a canonical structure of a projective variety over some...