TORSION CLASSES IN THE COHOMOLOGY OF KHT SHIMURA VARIETIES

Pascal Boyer (1, 2, 3)

1 UP13 - Université Paris 13
2 USPC - Université Sorbonne Paris Cité
3 LAGA - Laboratoire Analyse, Géométrie et Applications

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.

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Pascal Boyer. TORSION CLASSES IN THE COHOMOLOGY OF KHT SHIMURA VARIETIES. Mathematical Research Letters, In press, 18, pp.10001 - 100. ⟨hal-01667055⟩