Lafforgue's theorem, proved by Laurent Lafforgue, completes the Langlands program for general linear groups over algebraic function fields. It establishes a correspondence, a bijection between cuspidal automorphic representations of these groups and representations of their Galois groups, that preserves L-functions at every place of the field. The result carries substantial consequences for number theory, including implications for the Ramanujan-Petersson conjecture and for a conjecture of Deligne concerning irreducible l-adic representations with a finite-order determinant character. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
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StatementCompletes the Langlands program for general linear groups over algebraic function fields, giving a correspondence between automorphic forms on these groups and representations of Galois groups. 1 Classification
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1. Lafforgue's theorem (Wikipedia)
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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
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