  When the level at $l$ of a Shimura variety of Kottwitz-Harris-Taylor is not
maximal, its cohomology with coefficients in a $\overline{\mathbb Z}_l$-local
system isn't in general torsion free. In order to prove torsion freeness
results of the cohomology, we localize at a maximal ideal $\mathfrak m$ of the
Hecke algebra. We then prove a result of torsion freeness resting either on
$\mathfrak m$ itself or on the Galois representation $\overline \rho_{\mathfrak
m}$ associated to it. Concerning the torsion, in a rather restricted case than
the work of Caraiani-Scholze, we prove that the torsion doesn't give new Satake
parameters systems by showing that each torsion cohomology class can be raised
in the free part of the cohomology of a Igusa variety.
