论文标题
统一的Shimura曲线上的特殊周期
Special cycles on unitary Shimura curves at ramified primes
论文作者
论文摘要
In this paper, we study special cycles on the Krämer model of $\mathrm{U}(1,1)(F/F_0)$-Rapoport-Zink spaces where $F/F_0$ is a ramified quadratic extension of $p$-adic number fields with the assumption that the $2$-dimensional hermitian space of special quasi-homomorphisms is anisotropic.在这种情况下，我们写下了这些特殊周期的分解，并证明了Kudla-Ropoport的猜想。然后，我们应用局部结果来计算单一shimura曲线上特殊周期的交点数，并将这些交叉数与某些Eisenstein系列中心衍生物的傅立叶系数联系起来。
In this paper, we study special cycles on the Krämer model of $\mathrm{U}(1,1)(F/F_0)$-Rapoport-Zink spaces where $F/F_0$ is a ramified quadratic extension of $p$-adic number fields with the assumption that the $2$-dimensional hermitian space of special quasi-homomorphisms is anisotropic. We write down the decomposition of these special cycles and prove a version of Kudla-Rapoport conjecture in this case. We then apply the local results to compute the intersection numbers of special cycles on unitary Shimura curves and relate these intersection numbers to Fourier coefficients of central derivatives of certain Eisenstein series.
