In mathematics, Lafforgue's theorem, due to Laurent Lafforgue, completes the Langlands program for general linear groups over algebraic function fields, by giving a correspondence between automorphic forms on these groups and representations of Galois groups.
The Langlands conjectures were introduced by Langlands (1967, 1970) and describe a correspondence between representations of the Weil group of an algebraic function field and representations of algebraic groups over the function field, generalizing class field theory of function fields from abelian Galois groups to non-abelian Galois groups.