Abstract
In this paper, we proved a local arithmetic Siegel-Weil formula for a U ( 1 , 1 ) U(1, 1) -Shimura variety at a ramified prime, a.k.a. a Kudla-Rapoport conjecture at a ramified case. The formula needs to be modified from the original Kudla-Rapoport conjecture. In the process, we also give an explicit decomposition of the special divisors of the Rapoport-Zink space of unitary type ( 1 , 1 ) (1, 1) (KrÀmer model). A key ingredient is to relate the Rapoport-Zink space to the Drinfeld upper plane.
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