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This article has a weird claim on top, highlighted in yellow (see the second line):
Redirected from “local Langlands correspondence”.
Note: local Langlands conjecture and local Langlands conjecture both redirect for “local Langlands correspondence”.
(well, I made the error message go away. But it remains true that this error message was weird.)
I agree that the error message is confusing! It comes from Instiki. Eventually I will move the handling of redirects out of the old Instiki.
Added pointer to
It is curious that our quest was to understand the local Langlands correspondence in an arithmetic setting, for potentially very ramified representations, and eventually we solved it by relating it to the global Langlands correspondence in a geometric setting, in the everywhere unramified setting.
You have a lonely “For” above the reference. Probably some comment intended but missing.
Oh yes, I was going to find something pithy to say, but then forgot. I’ll add
For an approach via the Fargues–Fontaine curve…
We’ve discovered at least that this paper uses the tangent $(\infty, 1)$-topos to condensed spaces, from this MO answer.
There’s probably still a world to tap into of condensed differential cohesion, but perhaps that will have to wait.
Thanks for making all these edits, Anton! It’s much appreciated.
Sounds like you want a page global Langlands correspondence. Do you know how to create a new page? Let me know if I should do it.
In the Definition-section, I have taken the liberty of stating again the assumption that $G$ denotes a reductive group (if that’s the case, please check).
Have added numbered Definition-environments and some cross-pointers.
Have hyperlinked technical terms, by enclosing them in double square brackets [[...]]
:
e.g. p-adic field, residue field, class field theory
also for basic ones (such as inverse image, linear representation, irrep, invariant subspace, subgroup),
would it be better to change the page name from “local Langlands conjecture” to “local Langlands correspondence”
I don’t know. If you are expert on these topics and have reason to prefer one over the other, then you are invited to change it.
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