  A particular case of Bergeron-Venkatesh's conjecture predicts that torsion
classes in the cohomology of Shimura varieties are rather rare. According to
this and for Kottwitz-Harris-Taylor type of Shimura varieties, we first
associate to each such torsion class an infinity of irreducible automorphic
representations in characteristic zero, which are pairwise non isomorphic and
weakly congruent. Then, using completed cohomology, we construct torsion
classes in regular weight and then deduce explicit examples of such automorphic
congruences.
