Apologies if this question has already been dealt with on MO. I am wondering about the status of the global Langlands conjectures for $GL_2$ over the rational numbers. How close is humanity to the ...
My question, roughly speaking is, what happened to the function fields Langlands conjecture? I understand around 2000 (or slightly earlier perhaps), Lafforgue proved the function fields Langlands ...
Apologies in advance if this is a bit too simple to ask here, but I think I'm probably more likely to get an answer here than at stackexchange. I've been trying to learn the basics of the Langlands ...
Geometric class field theory (curves over a finite field) has been generalized to higher dimensional varieties over a finite field (and other arithmetical fields). Some of the key names here are Lang, ...