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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 maximal ideal $mathfrak m$ of $mathbb T$, appear to be free. In this work, we obtain the same result for $mathfrak m$ such that its associated galoisian $overline{mathbb F}_l$-representation $overline{rho_{mathfrak m}}$ is irreducible.
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
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
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 determine the irreducible components of Igusa varieties for Shimura varieties of Hodge type and use that to determine the irreducible components of central leaves. In particular, we show that the discrete Hecke-orbit conjecture is false in general
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