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arXiv · 2011.01356

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

Qiao He·Yousheng Shi·Tonghai Yang
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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 gives an explicit decomposition of the special divisors of the Rapoport-Zink space of unitary type $(1, 1)$ (Kr\"amer model). A key ingredient is to relate the Rapoport-Zink space to the Drinfeld upper plane.

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Qiao He, Yousheng Shi, Tonghai Yang. 2020-11-02. The Kudla-Rapoport conjecture at a ramified prime for $U(1, 1)$. https://arxiv.org/abs/2011.01356

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