Higher reciprocity laws

**15**

votes

**2**answers

878 views

### Status of (Global) Langlands Conjecture for $GL_2$ over $\mathbb{Q}$

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 ...

**13**

votes

**1**answer

2k views

### What is the current status of the function fields Langlands conjectures?

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 ...

**12**

votes

**1**answer

923 views

### Understanding the “idea” behind 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 ...

**5**

votes

**1**answer

826 views

### Langlands conjectures in higher dimensions

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, ...