Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2309.12413 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
Table des matières:
- We prove the cohomological version of the Sarnak--Xue Density Hypothesis for $SO_{5}$ over a totally real field and for inner forms split at all finite places. The proof relies on recent lines of work in the Langlands program: (i) Arthur's Endoscopic Classification of Representations of classical groups, extended to inner forms by Taïbi and its explicit description for $SO_{5}$ by Schmidt, and (ii) the Generalized Ramanujan--Petersson Theorem, proved for cohomological self-dual cuspidal representations of general linear groups. We give applications to the growth of cohomology of arithmetic manifolds, density-Ramanujan complexes, cutoff phenomena and optimal strong approximation.