  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 works of Laumon and Morel.
