Intersection Complex on the Baily-Borel Compactification of Siegel Modular Variety
| PU/IAS NUMBER THEORY | |
| Topic: | Intersection Complex on the Baily-Borel Compactification of Siegel Modular Variety |
| Speaker: | Sophie Morel |
| Affiliation: | Université Paris 11, France and Member, School of Mathematics |
| Date: | Thursday, November 16 |
| Time/Room: | 4:30pm - 5:30pm/Princeton University, Fine Hall 214 |
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.