Whenever I read a statement of the Langlands conjectures for a reductive group $G$, they are formulated in terms of the Langlands dual group, which is essentially the reductive group over $\mathbb{C}$ whose root datum is dual to that of $G$.

Instead of $\mathbb{C}$ we could use any separably closed field to obtain a "dual group”. Is there a compelling reason why the conjectures are not formulated in this generality?

notseparably closed). $\endgroup$