Kudla-Rapoport conjecture at a ramified prime.
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 a surprisingly simple proof of the modified conjecture by taking partial Fourier transform. This is a joint work with Chao Li, Yousheng Shi and Tonghai Yang.