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On the cohomology of certain PEL-type Shimura varieties

Mantovan, Elena (2005) On the cohomology of certain PEL-type Shimura varieties. Duke Mathematical Journal, 129 (3). pp. 573-610. ISSN 0012-7094. doi:10.1215/S0012-7094-05-12935-0.

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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.

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Additional Information:© 2005 Duke University Press. Received 26 November 2003. Revision received 9 November 2004. The author thanks Frans Oort and Richard Taylor for their continuous interest and suggestions.
Issue or Number:3
Classification Code:2000 Mathematics Subject Classification. Primary 11G18, 11F70; Secondary 14G35, 14L05.
Record Number:CaltechAUTHORS:20150424-130425079
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Official Citation:Mantovan, Elena. On the cohomology of certain PEL-type Shimura varieties. Duke Math. J. 129 (2005), no. 3, 573--610. doi:10.1215/S0012-7094-05-12935-0.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:56962
Deposited By: George Porter
Deposited On:24 Apr 2015 20:18
Last Modified:10 Nov 2021 21:06

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