Monodromy of the perverse sheaf of vanishing cycles of some simple Shimura varieties and applications
Monodromy of the perverse sheaf of vanishing cycles of some simple Shimura varieties and applications
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一些简单志村品种的消失周期反常束的单峰性及其应用
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发表时间：
2005
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通讯作者：
P. Boyer
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作者：
P. Boyer
在Harris和Taylor的书中研究的Kottwitz的简单Shimura簇的几何情形中，我们描述了消失圈复形的单值滤除及其谱序列，特别证明了这种滤除与权值1到移位一致.利用Berkovich-Fargues定理，我们导出了Deligne-Carayol模型的局部单值滤过的描述。在应用中，我们得到了某些酉群的上同调自守表示的局部分支的描述，两个酉群之间的整体Jacquet-Langlands对应，以及这些Shimura簇的上同调的权单值猜想的证明.
In the geometric situation of the simple Shimura varieties of Kottwitz studied in Harris and Taylor's book, we describe the monodromy filtration of the vanishing cycles complex and the spectral sequence associated to it. We prove in particular that this filtration coincides with the weight one up to shift. Thanks to the Berkovich-Fargues' theorem, we deduce the description of the local monodromy filtration of the Deligne-Carayol model. In application, we obtain the description of the local components of cohomological automorphic representations of certains unitary groups, a global Jacquet-Langlands correspondence between two such groups and a proof of the weight-monodromy conjecture for the cohomology of these Shimura varieties.