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In the geometric situation of some simple unitary Shimura varieties studiedby Harris and Taylor, I have built two filtrations of the perverse sheaf ofvanishing cycles. The graduate of the first are the $p$-intermediate extensionof some local Harris-Taylor's local systems, while for the second, obtained byduality, they are the $p+$-intermediate extensions. In this work, we describethe difference between these $p$ and $p+$ intermediate extension. Precisely, weshow, in the case where the local system is associated to an irreduciblecuspidal representation whose reduction modulo $l$ is supercuspidal, that thetwo intermediate extensions are the same. Otherwise, if the reduction modulo$l$ is just cuspidal, we describe the $l$-torsion of their difference.

Sur les extensions interm\'ediaires des syst\`emes locaux d'Harris-Taylor