Geometric Langlands correspondence

In mathematics, the geometric Langlands correspondence is a reformulation of the Langlands correspondence obtained by replacing the number fields appearing in the original number theoretic version by function fields and applying techniques from algebraic geometry. The geometric Langlands correspondence relates algebraic geometry and representation theory.

The specific case of the geometric Langlands correspondence for general linear groups over function fields was proven by Laurent Lafforgue in 2002, where it follows as a consequence of Lafforgue's theorem.