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 recent work of Kudla-Rapoport on unitary Shimura varieties. Our main result shows that these two families are related by (a formal version of) the Shimura lift.