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Jan 17 at 12:48 vote accept Coherent Sheaf
Jan 17 at 12:46 comment added Coherent Sheaf In section 5 of this article personal.math.ubc.ca/~cass/research/pdf/miyake.pdf, I believe they are doing the same thing as you suggested, but just below the "Langlands Lemma", he says $\hat{G}$-conjugacy classes in $\hat{G}\times$ Frob is the same as ${}^LG$-conjugacy classes. But I am not sure that statement is correct.
Jan 17 at 12:39 comment added Coherent Sheaf When you say Borel's article, do you mean the one titled "Automorphic L-functions"?
Jan 17 at 7:02 history answered David Loeffler CC BY-SA 4.0