# The global nilpotent variety is Lagrangian

@article{Ginzburg1997TheGN, title={The global nilpotent variety is Lagrangian}, author={Victor Ginzburg}, journal={Duke Mathematical Journal}, year={1997}, volume={109}, pages={511-519} }

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…

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