Kudla-Rapoport Conjecture for Krämer Models

The Kudla-Rapoport conjecture, proved jointly with Wei Zhang, is a precise identity relating arithmetic intersection numbers of special cycles on unitary Shimura varieties with good reduction and central derivatives of Siegel Eisenstein series. We discuss how to formulate and prove an analogous identity for certain unitary Shimura varieties with bad reduction (Krämer models at ramified places). We will motivate these conjectures and highlight interesting new phenomena in the presence of bad reduction. This is joint work with Qiao He, Yousheng Shi and Tonghai Yang.

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