UCLA

In this paper, we compute the cohomology with compact supports of a Picard

modular surface as a virtual module over the product of the appropriate Galois

group and the appropriate Hecke algebra. We use the method developed by Ihara,

Langlands, and Kottwitz: comparison of the Grothendieck-Lefschetz formula and

the Arthur-Selberg trace formula. Our implementation of this method takes as

its starting point the work of Laumon and Morel.