Vertical Distribution Relations for Special Cycles on Unitary Shimura Varieties
Vertical Distribution Relations for Special Cycles on Unitary Shimura Varieties
复制标题
单一志村品种特殊周期的垂直分布关系
DOI：
10.1093/imrn/rny119
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发表时间：
2015
影响因子：
1
通讯作者：
Dimitar Jetchev
中科院分区：
文献类型：
--
作者：
Reda Boumasmoud;Ernest Hunter Brooks;Dimitar Jetchev
我们考虑了依附于酉群的三维Shimura簇上的圈，这些圈定义在复乘(CM)域$E$的扩张上，这出现在Gan等人的猜想的背景下。[6]。我们建立了这些圈在$E$的反闭扩张上的垂直分布关系，补充了[8]的水平分布关系，并利用它定义了这些域上的范数相容圈族，从而得到了类似于由Heegner点构造的Heegner$\Lambda$-模的普适范数结构。
We consider cycles on three-dimensional Shimura varieties attached to unitary groups, defined over extensions of a complex multiplication (CM) field $E$, which appear in the context of the conjectures of Gan et al. [6]. We establish a vertical distribution relation for these cycles over an anticyclotomic extension of $E$, complementing the horizontal distribution relation of [8], and use this to define a family of norm-compatible cycles over these fields, thus obtaining a universal norm construction similar to the Heegner $\Lambda $-module constructed from Heegner points.