Abstract
Since Serre [Se3] first conjectured the possibility of attaching Galois representations to higher weight modular forms for GL(2), and Deligne [D] proved it, this notion has been expanded to apply to a large class of automorphic forms on more general reductive groups. Clozel [Cl1], following Langlands [La], has given a precise conjecture for GL(n), recalled below. I shall refer to it as the “central conjecture”. Further discussion of the history, which should be traced backwards at least to work of Eichler, Shimura, and Weil, may be found in the last section of [Se3] and the introduction to [Cl1]. One should add the remark that Serre [Se4] seems to have been the first to propose that all L-functions of motives might be L-functions of automorphic forms.
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Ash, A. (1992). Galois representations and cohomology of GL(n, ℤ). In: David, S. (eds) Séminaire de Théorie des Nombres, Paris, 1989–90. Progress in Mathematics, vol 102. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-4269-5_2
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