The symmetric-power automorphy conjecture

Let $k$ be a global field and let $\Pi$ be a cuspidal automorphic representation of ${\rm GL}_n(\mathbb{A}_k)$. Symmetric-power automorphy conjecture. For every $n$, the symmetric-power lift $\operatorname{Sym}^n(\Pi)$ is also automorphic.

This conjecture is described as an important open problem over number fields and as a consequence of Lafforgue's work over function fields. The source also notes that Langlands observed that automorphy of symmetric powers implies the Ramanujan conjecture.