| Résume | For a reductive group G over a local non-archimedean field K one can mimic constructions from the classical Deligne-Lusztig theory by using the loop space functor. In special cases - attached to G = inner form of GLn, and Coxeter elements in the Weyl group - we show that the resulting fpqc-sheaves on algebras over the residue field of K are representable by schemes. Their ℓ-adic cohomology realizes many irreducible supercuspidal representations of G, notably almost all among those whose L-parameter factors through an unramified elliptic maximal torus of G. This gives a purely local, purely geometric and - in a sense - quite explicit way to realize special cases of the local Langlands and Jacquet-Langlands correspondences. |
