Motives and Automorphic Representations Laurent Clozel
Motives and automorphic representations Laurent Clozel To cite this version: Laurent Clozel. Motives and automorphic representations. 2006. hal-01019707 HAL Id: hal-01019707 https://hal.archives-ouvertes.fr/hal-01019707 Preprint submitted on 7 Jul 2014 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Motives and automorphic representations L. Clozel Introduction These are, slightly expanded, the notes of my 3-hour lecture at IHES in July 2006. The organizers had assigned me two tasks. First, to give an overview of the conjectural relations between the motives defined by algebraic varieties over number fields and automorphic forms { here, automorphic forms on GL(n). (The relation is mediated by two other kinds of objects, namely, Galois representations and L-functions). Secondly, to furnish { in a more leisurely way, at least for the topics I chose to present, than in his paper { the prerequisites necessary to understand the automorphic part of R. Taylor's beautiful lecture, \Galois representations", at the Beijing ICM (2002)1. These are rather succinct notes, so it was certainly not possible to present in detail, with proofs, the basic material: the reader will have to consult the standard references [36, 44, 18].
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