Green forms and the arithmetic Siegel–Weil formula
Green forms and the arithmetic Siegel–Weil formula
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绿色形式和算术西格尔-韦尔公式
DOI：
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发表时间：
2018
影响因子：
3.1
通讯作者：
Siddarth Sankaran
中科院分区：
文献类型：
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作者：
Luis E. García;Siddarth Sankaran
我们构造了正交酉型Shimura变量中所有余维的特殊环的自然Green形式，并且对于$$ mathm {O}(p,2)$$O（p,2）和$$ mathm {U}(p,1)$$U（p,1）的紧型Shimura变量，我们证明了得到的局部阿基米德高度对与Siegel Eisentein级数的导数的特殊值有关。Kudla的一个猜想将这些导数与特殊环的算术交点联系起来，我们的结果解决了他的猜想中涉及局部阿基米德高度的部分。
We construct natural Green forms for special cycles in orthogonal and unitary Shimura varieties, in all codimensions, and, for compact Shimura varieties of type $$mathrm {O}(p,2)$$O(p,2) and $$mathrm {U}(p,1)$$U(p,1), we show that the resulting local archimedean height pairings are related to special values of derivatives of Siegel Eisentein series. A conjecture put forward by Kudla relates these derivatives to arithmetic intersections of special cycles, and our results settle the part of his conjecture involving local archimedean heights.