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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.
We study the torsion cohomology classes of Shimura varieties of type Kottwitz-Harris-Taylor and we show that up to an arbitrary place one can raise them to an automorphic representation. In application, to any mod $l$ system of Hecke eigenvalues ap
A particular case of Bergeron-Venkateshs 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 tors
Let $Sh_K(G,mu)$ be a Shimura variety of KHT type, as introduced in Harris-Taylor book, associated to some similitude group $G/mathbb Q$ and a open compact subgroup $K$ of $G(mathbb A)$. For any irreducible algebraic $overline{mathbb Q}_l$-representa
We investigate the correspondence between holomorphic automorphic forms on the upper half-plane with complex weight and parabolic cocycles. For integral weights at least 2 this correspondence is given by the Eichler integral. Knopp generalized this t
The integral model of a GU(n-1,1) Shimura variety carries a universal abelian scheme over it, and the dual top exterior power of its Lie algebra carries a natural hermitian metric. We express the arithmetic volume of this metrized line bundle, define