  The 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.
