Abstract: First, I will motivate and state the Kudla–Rapoport conjecture for Kramer models of unitary Rapoport–Zink spaces at ramified primes. It is a precise identity between arithmetic intersection numbers of special cycles on Kramer models and modified derived local densities of hermitian forms. Then I will talk about the difficulties of this case compared with the unramified case, and illustrate the new innovations that used to prove this conjecture. As an application,
we obtain the arithmetic Siegel–Weil formula unconditionally for unitary Shimura varieties associated with unimodular hermitian lattices over certain imaginary quadratic fields.
This is a joint work with Chao Li, Yousheng shi and Tonghai Yang.
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