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Complexes pondérés sur les compactifications de Baily-Borel: Le cas des variétés de Siegel

Author(s): Sophie Morel
Journal: J. Amer. Math. Soc. 21 (2008), 23-61.
MSC (2000): Primary 11F75; Secondary 11G18, 14F20
Posted: June 9, 2006
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Abstract: In this work, we calculate the trace of a Hecke correspondance composed with a power of the Frobenius endomorphism on the fibre of the intersection complexes of the Baily-Borel compactification of a Siegel modular variety.

Our main tool is Pink's theorem about the restriction to the strata of the Baily-Borel compactification of the direct image of a local system on the Shimura variety. To use this theorem, we give a new construction of the intermediate extension of a pure perverse sheaf as a weight truncation of the full direct image.

More generally, we are able to define analogs in positive characteristic of the weighted cohomology complexes introduced by Goresky, Harder and MacPherson.

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Additional Information:

Sophie Morel
Affiliation: Laboratoire de mathématique, Université Paris-Sud, bâtiment 425, 91405 Orsay Cedex, France
Address at time of publication: After September 1, 2006: School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540
Email: sophie.morel@math.u-psud.fr

DOI: 10.1090/S0894-0347-06-00538-8
PII: S 0894-0347(06)00538-8
Received by editor(s): November 11, 2005
Posted: June 9, 2006
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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