Torsion classes in the cohomology of KHT Shimura varieties

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 in the sense of [16]. Then, using completed cohomology, we construct torsion classes in regular weight and then deduce explicit examples of such automorphic congruences.

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Received 20 March 2017

Accepted 17 December 2017

Published 1 February 2019