| Résume | A local Shimura variety is a p-adic analogue of a Shimura variety. Its l-adic cohomology is expected to be related to the local Langlands correspondence. In the Lubin-Tate case, a supercuspidal representation appears only in the middle degree. In the GSp(4) case, a supercuspidal representation appears only in the degrees 3,4, and it appears in the degree 4 if and only if its L-parameter has non-trivial SL(2)-part. In this talk, I will explain my recent results in this direction for more general cases. |
