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The global nilpotent variety is Lagrangian

Victor Ginzburg
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Abstract

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.

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Victor Ginzburg. 2000-10-31. The global nilpotent variety is Lagrangian. https://arxiv.org/abs/alg-geom/9704005

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