DOCUMENTA MATHEMATICA, Vol. 18 (2013), 1403-1464

Siddarth Sankaran

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

2010 Mathematics Subject Classification: 14G35, 11G18, 11F30.

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