# On the Cohomology of Non-Compact Unitary Shimura Varieties

 SHIMURA VARIETIES AND TRACE FORMULA SEMINAR Topic: On the Cohomology of Non-Compact Unitary Shimura Varieties Speaker: S. Morel Affiliation: Member, School of Mathematics Date: Friday, October 3 Time/Room: 2:00pm - 3:30pm/West Bldg. Lecture Hall

In this talk, I will explain how the method originally developed by Ihara, Langlands and Kottwitz to compute the cohomology of a Shimura variety (use the Grothendieck-Lefschetz fixed point formula in positive characteristic to calculate the trace on the cohomology of a power of Frobenius at a good place times a Hecke operator trivial at that place, and then compare the result with Arthur's trace formula) applies to intersection cohomology of the Satake-Baily-Borel compactification of unitary Shimura varieties. I will also present applications (to the calculation of the L-function of the intersection complex and, time permitting, to the construction of Galois representations associated to (certain) automorphic representations).