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

He, Qiao; Shi, Yousheng; Yang, Tonghai

doi:10.1090/tran/8845

The Kudla-Rapoport conjecture at a ramified prime for $U(1, 1)$
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by Qiao He, Yousheng Shi and Tonghai Yang PDF

Trans. Amer. Math. Soc. 376 (2023), 2257-2291 Request permission

Abstract:

In this paper, we proved a local arithmetic Siegel-Weil formula for a $U(1, 1)$-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 $(1, 1)$ (Krämer model). A key ingredient is to relate the Rapoport-Zink space to the Drinfeld upper plane.

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