Geometric Langlands correspondence

In mathematics, the geometric Langlands correspondence relates algebraic geometry and representation theory. It 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.^[1] The geometric Langlands conjecture asserts the existence of the geometric Langlands correspondence.

The existence of the geometric Langlands correspondence in the specific case of general linear groups over function fields was proven by Laurent Lafforgue in 2002, where it follows as a consequence of Lafforgue's theorem.^[2]