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• W2162750147 abstract "In this article we study the local geometry at a prime p of PEL-type Shimura varieties for which there is a hyperspecial level subgroup. We consider the Newton polygon stratification of the special fiber at p of Shimura varieties and show that each Newton polygon stratum can be described in terms of the products of the reduced fibers of the corresponding PEL-type Rapoport-Zink spaces with certain smooth varieties (which we call Igusa varieties) and of the action on them of a p-adic group that depends on the stratum. We then extend our construction to characteristic zero and, in the case of bad reduction at p, use it to compare the vanishing cycle sheaves of the Shimura varieties to those of the Rapoport-Zink spaces. As a result of this analysis, in the case of proper Shimura varieties we obtain a description of the l-adic cohomology of the Shimura varieties in terms of the l-adic cohomology with compact supports of the Igusa varieties and of the Rapoport-Zink spaces for any prime l≠p." @default.
• W2162750147 created "2016-06-24" @default.
• W2162750147 creator A5050127392 @default.
• W2162750147 date "2005-09-15" @default.
• W2162750147 modified "2023-09-30" @default.
• W2162750147 title "On the cohomology of certain PEL-type Shimura varieties" @default.
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• W2162750147 doi "https://doi.org/10.1215/s0012-7094-05-12935-0" @default.
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