11/16/2006

Sophie Morel
Institute for Advanced Study

Intersection complex on the Baily-Borel compactification of a Siegel modular variety

In this talk, I will explain how to compute the trace of a power of the Frobenius endomorphism on the intersection cohomology of the Baily-Borel compactification of a Siegel modular variety.
The main tools are :
- Kottwitz's calculation of the number of points of PEL Shimura varieties over finite fields;
- a theorem of Pink about the direct image in the Baily-Borel compactification of a local system on a Shimura variety;
- a new construction of the intermediate extension of a pure perverse sheaf as a weight truncation of the full direct image.