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.