Test functions for Shimura varieties: the Drinfeld case
Test functions for Shimura varieties: the Drinfeld case
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Shimura 品种的测试函数：Drinfeld 案例
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发表时间：
2001
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通讯作者：
T. Haines
中科院分区：
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作者：
T. Haines
设(G，X，K)是有反域E的Shimura基准面，选择E的素数p和p上的素理想p，设Kp⊂G(Qp)是一个重指的子群.还假设G在Qup上分裂，因此Ep是Qp的非分支扩张。设SK表示对应Shimura簇的OE，p上的一个模型。那么，SK的还原情况往往很糟糕。一般来说，特殊纤维的奇点是非常复杂的，必须以某种方式理解才能研究Shimura变种的局部Zeta函数。Rapoport[13]概述了解决这个问题的策略。第一部分是找到一种便捷的表达方式
Let (G, X, K) be a Shimura datum with reflex field E. Choose a prime number p and a prime ideal p of E lying over p. Suppose that Kp ⊂ G(Qp) is a parahoric subgroup. Also assume that G splits over Qun p , and hence that Ep is an unramified extension of Qp. Let SK denote a model over OE,p of the corresponding Shimura variety. Then it is often the case that SK has bad reduction. The singularities of the special fiber are very complicated in general, and somehow must be understood in order to study the local zeta function of the Shimura variety at p. Rapoport [13] has outlined a strategy to attack this problem. The first part is to find a convenient way to express