Galois irreducibility implies cohomology freeness for KHT Shimura varieties
Résumé
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 paper 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.
Origine : Fichiers produits par l'(les) auteur(s)
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