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Chtoucas de Drinfeld et correspondance de Langlands

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On démontre la correspondance de Langlands pour GL r sur les corps de fonctions. La preuve généralise celle de Drinfeld en rang 2 : elle consiste à réaliser la correspondance en rang r dans la cohomologie ℓ-adique des variétés modulaires de chtoucas de Drinfeld de rang r.


One proves Langlands’ correspondence for GL r over function fields. This is a generalization of Drinfeld’s proof in the case of rank 2 : Langlands’ correspondence is realized in ℓ-adic cohomology spaces of the modular varieties classifying rank r Drinfeld shtukas.

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Oblatum 13-X-2000 & 7-VI-2001¶Published online: 12 October 2001

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Lafforgue, L. Chtoucas de Drinfeld et correspondance de Langlands. Invent. math. 147, 1–241 (2002).

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Code matière AMS (2000)