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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 $overline{mathbb Q}_l$-representation $xi$ of $G$, let $V_xi$ be the $mathbb Z_l$-local system on $Sh_K(G,mu)$. From my paper about p-stabilization, we know that if we allow the local component $K_l$ of $K$ to be small enough, then there must exists some non trivial cohomology classes with coefficient in $V_xi$. The aim of this paper is then to construct explicitly such torsion classes with the control of $K_l$. As an application we obtain the construction of some new automorphic congruences between tempered and non tempered automorphic representations of the same weight and same level at $l$.
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
Given a KHT Shimura variety provided with an action of its unramified Hecke algebra $mathbb T$, we proved in a previous work, see also the work of Caraiani-Scholze for other PEL Shimura varieties, that its localized cohomology groups at a generic max
We prove that there is a natural plectic weight filtration on the cohomology of Hilbert modular varieties in the spirit of Nekovar and Scholl. This is achieved with the help of Morels work on weight t-structures and a detailed study of partial Froben
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,
In this article, we generalize the work of H.Hida and V.Pilloni to construct $p$-adic families of $mu$-ordinary modular forms on Shimura varieties of Hodge type $Sh(G,X)$ associated to a Shimura datum $(G,X)$ where $G$ is a connected reductive group