Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published September 15, 2005 | Submitted
Journal Article Open

On the cohomology of certain PEL-type Shimura varieties

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.

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.

Attached Files

Submitted - PEL.pdf

Files

PEL.pdf
Files (344.8 kB)
Name Size Download all
md5:b6ae094240c16980534b6055a6d7ef78
344.8 kB Preview Download

Additional details

Created:
August 19, 2023
Modified:
October 23, 2023