2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147218The purpose of this note is to present a short elementary proof of a theorem due to Faltings and Laumon, saying that the global nilpotent cone is a Lagrangian substack in the cotangent bundle of the moduli space of G-bundles on a complex compact curve. This result plays a crucial role in the Geometric Langlands program, due to Beilinson-Drinfeld, since it insures that the D-modules on the moduli space of G-bundles whose characteristic variety is contained in the global nilpotent cone are automatically holonomic, hence, e.g. have finite length.LaTeX, 9pp. Final version, to appear in Duke Math. JAlgebraic GeometryDifferential GeometryQuantum Algebratext