Résume | By Harris-Taylor's work with global methods, we know that the etale cohomology groups of coverings of Lubin-Tate space incorporate the local Langlands correspondence for $GL_n$ over local fields. We recover this result in the special case of depth $0$ in a purely local way by computing a resolution of the corresponding formal scheme. It turns out that we can geometrically relate it to the theory of Deligne- Lusztig, as is naturally expected from the form of representations. |