Automorphic congruences and torsion in the cohomology of a simple   unitary Shimura variety
  We first give a relative flexible process to construct torsion cohomology classes for Shimura varieties of Kottwitz-Harris-Taylor type with coefficient in a non too regular local system. We then prove that associated to each torsion cohomology class, there exists a infinity of irreducible automorphic representations in characteristic zero, which are pairwise non isomorphic and weakly congruent. 
Pascal Boyer
math.NT