  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 Galois $\overline{\mathbb F}_l$-representation
$\overline{\rho_{\mathfrak m}}$ is irreducible, under the hypothesis that
$[F(\exp(2i\pi/l):F]>d$ where $F$ is the reflex field, $d$ the dimension of the
KHT Shimura variety and $l$ the residual characteristic.
