Special cycles on unitary Shimura curves at ramified primes

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...

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

Automorphisms and Reduction of Heegner Points on Shimura Curves at Cerednik-drinfeld Primes

Let X be a Shimura curve of genus at least 2. Exploiting Čerednik-Drinfeld’s description of the special fiber of X and the specialization of its Heegner points, we show that, under certain technical conditions, the group of automorphisms of X corresponds to its group of Atkin-Lehner involutions.

Modularity of Generating Functions of Special Cycles on Shimura Varieties

Modularity of Generating functions of Special Cycles on Shimura Varieties