分野別セミナー

It is widely believed that the l-adic cohomology of Rapoport-Zink spaces realize the local Langlands and Jacquet-Langlands correspondences. For the Lubin-Tate spaces or Drinfeld upper half spaces, it was established by Harris-Taylor and Boyer. It turns out that supercuspidal representations of GL(n) appears only in the middle degree cohomology. However, this is not true for more general Rapoport-Zink spaces. In this talk, we consider supercuspidal representations in the cohomology of the Rapoport-Zink space for GU(3). A new phenomenon is that certain supercuspidal representations, which are related to non-tempered endoscopy, appear outside the middle degree. Similar results can be obtained for GSp(4) assuming some form of Arthur's conjecture. This is a joint work with Yoichi Mieda.