论文标题
de de rham derevêtementModérédel'Espace de drinfeld
Cohomologie de de Rham du revêtement modéré de l'espace de Drinfeld
论文作者
论文摘要
在本文中，我们研究了Drinfel'd Tower的第一个封面的De Rham共同体。特别是，我们获得了一个纯粹的本地证据，即超级悬浮部分通过将其与某些Deligne-lusztig品种的刚性共同体进行比较，从而实现了$ {\ rm gl} _n $的本地jacquet-langlands对应。如果我们忘记了Weil组的动作，获得的表示形式类似于$ \ ell $ - adic共同体中出现的表示形式。证明依赖于Grosse-Klönne的切除结果的概括，以及对第一封面的明确描述作为作者对先前工作的循环封面。
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 ${\rm GL}_n$ 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.
