Kudla-Rapoport conjecture predicts that there is an identity between the intersection number of special cycles on unitary Rapoport-Zink space and the derivative of local density of certain Hermitian form. However, the original conjecture was only formulated for RZ space with hyperspecial level structure over unramified primes . In this talk, I will motivate the original conjecture and discuss how to modify it at a ramified prime. Finally, I will sketch how to verify the modified conjecture for n=3. This is a joint work with Qiao He and Tonghai Yang.

Yousheng Shi (University of Wisconsin-Madison)