The finite-to-one surjective local Langlands correspondence

Let $F$ be a $p$-adic field, let $W_F'$ be its Weil–Deligne group, and let $G$ be a connected reductive $p$-adic group. Let $\Pi(G/F)$ be the set of isomorphism classes of irreducible smooth representations of $G(F)$, and let $\Phi(G/F)$ be the set of $\hat{G}$-conjugacy classes of admissible Langlands parameters $\varphi:W_F'\rightarrow{}^LG$. Local Langlands conjecture. There is a finite-to-one surjective map $\Pi(G/F)\rightarrow\Phi(G/F)$ satisfying the desiderata of Borel's formulation. This is presented as the general conjectural form of the local Langlands correspondence; no resolution or restriction to a class of groups is supplied in the text.