The Stacks project

Remark 63.31.4. We now have, thanks to Lafforgue and many other mathematicians, complete theorems like this two above for $\text{GL}_ n$ and allowing ramification! In other words, the full global Langlands correspondence for $\text{GL}_ n$ is known for function fields of curves over finite fields. At the same time this does not mean there aren't a lot of interesting questions left to answer about the fundamental groups of curves over finite fields, as we shall see below.


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