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.
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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
Statement FormCharacterization Theorem 1 Lafforgue's Theorem
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Source Lafforgue's theorem (Wikipedia)
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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
In Branch: Number Theory, Lead
Lafforgue's theorem, due to Laurent Lafforgue, completes the Langlands program for general linear groups over algebraic function fields
Principal Result Of: Laurent Lafforgue, Lead sentence of the article on the result
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.
Proved By: Laurent Lafforgue, Lead
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.
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