2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160079We propose a proof for conjectures of Langlands, Shelstad and Waldspurger known as the fundamental lemma for Lie algebras and the non-standard fundamental lemma. The proof is based on a study of the decomposition of the l-adic cohomology of the Hitchin fibration into direct sum of simple perverse sheaves.197 pages, submittedAlgebraic Geometry14H60, 22E35 (Primary); 14F20 (Secondary)text