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 correspondence for $GL(n)$ in full generality (proving all aspects of the conjectures). Since then, what's happened to the function fields Langlands conjectures, and what work have people been doing in this direction? (Or has this field died out after Lafforgue's monumental achievement?)

I have been trying but haven't found a good reference for this, but since the function fields Langlands conjectures can be defined for all reductive groups (though I understand in some sense, it is not as "strong" as it is for $GL$ in the general case) - what is the status of these conjectures? Have partial results been obtained?

I understand that geometric Langlands is very intensely researched today, but I consider geometric Langlands as being slightly different (even though it is an analogue of the function fields Langlands correspondence - from reading Frenkel's article on geometric Langlands, my impression was not that geometric Langlands encapsulates all of the information in function fields Langlands conjectures), and I'm asking what work has been done since specifically on function fields Langlands. Or am I misunderstanding things and do the geometric Langlands conjectures actually encapsulate all the information from function fields Langlands as well?

I understand that the Fundamental Lemma has been proven recently, and that Lafforgue is doing some things relating to Langlands functoriality currently. Here's a related thread about Langlands functoriality: Where stands functoriality in 2009?..

1more comment