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What is the $p$-adic Langlands conjecture for $\mathbf{GL}_1$?
In the Boston conference on Fermat's Last Theorem (Summer 1995), Barry Mazur said (around 15m into the video) about class field theory that
If you are a number-theorist and you want to cheer ...
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Non-existence of "higher" Artin map
So rank $1$ local Langlands is special in as that it is given by the Artin map
$$\text{GL}_1(K)\to G_K^{ab},$$
whereas in the higher rank (to the best of my knowledge) there doesn't exist a map
$$\...