Cohomologie de de Rham du revêtement modéré de l'espace de Drinfeld

Abstract

In this article, we study the De Rham cohomology of the first cover in the Drinfel'd tower. In particular, we get a purely local proof that the supercuspidal part realizes the local Jacquet-Langlands correspondence for ${\mathrm{GL}}_n$ by comparing it to the rigid cohomology of some Deligne-Lusztig varieties. The representations obtained are analogous to the ones appearing in the $\ell$-adic cohomology if we forget the action of the Weil group. The proof relies on the generalization of an excision result of Grosse-Klönne and on the explicit description of the first cover as a cyclic cover obtained by the author on a previous work.

arXiv comment38 pages in French, new version : aknowledgement added and some typos in the abstract corrected

References in corpus (1)

• Theorie de Lubin-Tate non-abelienne et representations elliptiques