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Motives and automorphic forms: application of the functoriality principle. (Motifs et formes automorphes: Applications du principle de fonctorialit√©.) (French) Zbl 0705.11029
Automorphic forms, Shimura varieties, and L-functions. Vol. I, Proc. Conf., Ann Arbor/MI (USA) 1988, Perspect. Math. 10, 77-159 (1990).
[For the entire collection see Zbl 0684.00003.]
The paper under review deals with some consequences of Langlands’ general conjectures (sometimes theorems). Its main topic is the question whether an automorphic form on \(\mathrm{GL}(n)\) can be defined over a number field. As it is customary in the subject there are many conjectures and some theorems, whose proofs however tend to be too complicated to be given here.

MSC:
11F70 Representation-theoretic methods; automorphic representations over local and global fields
11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
14A20 Generalizations (algebraic spaces, stacks)