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I have been reading the book Fearless Symmetry by Ash and Gross.It talks about Langlands program, which it says is the conjecture that there is a correspondence between any Galois representation coming from the etale cohomology of a Z-variety and an appropriate generalization of a modular form, called an “automorphic representation".

Even though it appears to be interesting, I would like to know that are there any important immediate consequences of the Langlands program in number theory or any other field. Why exactly are the mathematicians so excited about this?

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    You can formulate the Langslands programme in any dimension. In dimension 1 it is equivalent to the main results of class field theory. That's one reason it is interesting. In dimension 2 it implies the infamous Taniyama-Shimura conjecture proved by Wiles. I don't know much else but a programme which already implies such big results in low dimension must be interesting, right?2011-10-09
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    Well,I know that 2-dimensional case implies TS conjecture. But are other any other important consequences?2011-10-09
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    @shaye, why "infamous"?2012-06-26
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    Please have a look at https://mathoverflow.net/questions/78247.2018-04-23

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