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首页> 外文期刊>Journal fur die Reine und Angewandte Mathematik >Special cycles on unitary Shimura varieties II: Global theory
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Special cycles on unitary Shimura varieties II: Global theory

机译:单一志村品种的特殊周期II:全球理论

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摘要

We introduce moduli spaces of abelian varieties which are arithmetic models of Shimura varieties attached to unitary groups of signature. (n - 1, 1). We define arithmetic cycles on these models and study their intersection behavior. In particular, in the non-degenerate case, we prove a relation between their intersection numbers and Fourier coefficients of the derivative at s = 0 of a certain incoherent Eisenstein series for the group U(n, n). This is done by relating the arithmetic cycles to their formal counterpart from part I [33] via non-archimedean uniformization, and by relating the Fourier coefficients to the derivatives of representation densities of hermitian forms. The result then follows from the main theorem of part I and a counting argument.
机译:我们介绍了阿贝尔变种的模数空间,阿贝尔变种是隶属于单一签名组的志村变种的算术模型。 (n-1,1)。我们在这些模型上定义算术循环,并研究它们的相交行为。特别是在非简并的情况下,我们证明了群U(n,n)的某个非相干爱森斯坦级数在s = 0时导数的交点数与傅里叶系数之间的关系。这是通过非算术统一将算术循环与其从第一部分[33]开始的形式对应关系以及将傅立叶系数与厄米形式的表示密度的导数相关联来完成的。然后,结果来自于第一部分的主定理和一个计数参数。

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