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arXiv · 2204.06363

Cohomologie de de Rham du rev\^etement mod\'er\'e de l'espace de Drinfeld

Damien Junger
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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 ${\rm GL}_n$ 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-Kl\"onne and on the explicit description of the first cover as a cyclic cover obtained by the author on a previous work.

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Damien Junger. 2022-04-13. Cohomologie de de Rham du rev\^etement mod\'er\'e de l'espace de Drinfeld. https://doi.org/10.1017/s1474748024000082

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