2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76530We prove a conjecture of Frenkel-Gaitsgory-Kazhdan-Vilonen on some exponential sums related to the geometric Langlands correspondence. Our main ingredients are the resolution of Lusztig scheme of lattices introduced by Laumon and the decomposition theorem of Beilinson-Bernstein-Deligne-Gabber.Latex, 14 pagesAlgebraic Geometrytext