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15 September 2005 On the cohomology of certain PEL-type Shimura varieties
Elena Mantovan
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Duke Math. J. 129(3): 573-610 (15 September 2005). DOI: 10.1215/S0012-7094-05-12935-0


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 lp.


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Elena Mantovan. "On the cohomology of certain PEL-type Shimura varieties." Duke Math. J. 129 (3) 573 - 610, 15 September 2005.


Published: 15 September 2005
First available in Project Euclid: 19 October 2005

zbMATH: 1112.11033
MathSciNet: MR2169874
Digital Object Identifier: 10.1215/S0012-7094-05-12935-0

Primary: 11F70 , 11G18
Secondary: 14G35 , 14L05

Rights: Copyright © 2005 Duke University Press


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Vol.129 • No. 3 • 15 September 2005
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