Torsion classes in the cohomology of KHT Shimura varieties

摘要

A particular case of Bergeron-Venkatesh's conjecture predicts that torsionclasses in the cohomology of Shimura varieties are rather rare. According tothis and for Kottwitz-Harris-Taylor type of Shimura varieties, we firstassociate to each such torsion class an infinity of irreducible automorphicrepresentations in characteristic zero, which are pairwise non isomorphic andweakly congruent. Then, using completed cohomology, we construct torsionclasses in regular weight and then deduce explicit examples of such automorphiccongruences.