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Current Status on Langlands Program

the ones which are algebraic at infinity in the case of number fields) is only a part of the Langlands program, essentially because it concerns just certain automorphic representations, and Langlands functoriality … For the functoriality for (non necessarily algebraic) automorphic representations, much less is known (Solvable base change for $\operatorname{GL}_n$ by Langlands and Arthur-Clozel, some transfer between …
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