• Corpus ID: 215768671

# Special cycles on unitary Shimura curves at ramified primes

@article{Shi2020SpecialCO,
title={Special cycles on unitary Shimura curves at ramified primes},
author={Yousheng Shi},
journal={arXiv: Algebraic Geometry},
year={2020}
}
• Yousheng Shi
• Published 13 April 2020
• Mathematics
• arXiv: Algebraic Geometry
In this paper, we study special cycles on the Kramer model of $\mathrm{GU}(1,1)(F)$ Rapoport-Zink spaces where $F$ is a ramified extension of $\mathbb{Q}_p$ with the assumption that the underlying hermitian form on the Dieudonne module of the framing object of the Rapoport-Zink space is aniostropic. We write down the decomposition of these special cycles and compute their intersection numbers. We then apply the local results to compute the intersection numbers of special cycles on unitary…
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SCIENTIA SINICA Mathematica
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In this paper, we first review and summarize some recent progress in Kudla program on unitary Shimura varieties. We show how the local arithmetic Siegel-Weil formula implies the global arithmetic
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In this paper, we propose a modified Kudla-Rapoport conjecture for the Krämer model of unitary Rapoport-Zink space over a ramified prime, which is a precise identity relating intersection numbers of
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• 2020
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 in a ramified case. The formula needs to be

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