The Kudla-Rapoport conjecture at a ramified prime for 𝑈(1,1)

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) (Krämer model). A key ingredient is to relate the Rapoport-Zink space to the Drinfeld upper plane.