2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63109We prove the Jacquet-Langlands local correspondence in non-zero characteristic, using the proof by Deligne, Kazhdan and Vignéras for the zero characteristic case and the theory of closed fields of Kazhdan. We also prove the orthogonality relations for an inner form of $GL_n$ in non-zero characteristic.to appear in Annales Scientifiques de l'École Normale SupérieureGroup Theorytext