Sankaran, Siddarth

Unitary cycles on Shimura curves and the Shimura lift. I

Doc. Math., J. DMV 18, 1403-1464 (2013)


Summary: 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 relates these two families by (a formal version of) the Shimura lift.

Mathematics Subject Classification

14G35, 11G18, 11F30