  This article is the $\mathrm{Z}_l$-version of my paper "Monodromie du
faisceau pervers des cycles \'evanescents de quelques vari\'et\'es de Shimura
simples" in Invent. Math. 2009 vol 177 pp. 239-280, where we study the
vanishing cycles of some unitary Shimura variety. The aim is to prove that the
cohomology sheaves of this complexe are free so that, thanks to the main
theorem of Berkovich on vanishing cycles, we can deduce that the
$\mathrm{Z}_l$-cohomology of the model of Deligne-Carayol is free. There will
be a second article which will be the $\mathrm{Z}_l$ version of my paper
"Conjecture de monodromie-poids pour quelques vari\'t\'es de Shimura unitaires"
in Compositio vol 146 part 2, pp. 367-403. The aim of this second article will
be to study the torsion of the cohomology groups of these Shimura varieties.
