The global Serre weight conjecture for unitary Galois representations

Fix an imaginary CM field $F$ with maximal totally real subfield $F^+$ such that every prime of $F^+$ above $p$ has residue field ${\mathbb{F}}_p$ and splits in $F$. Let $S$ be the set of places of $F$ above $p$. Write $({\mathbb{Z}}^2_+)_0^S$ for the tuples $a=(a_w)_{w\in S}$ satisfying $a_{w,1}+a_{w^c,2}=0$ for every $w\in S$, and call $a$ a Serre weight if $p-1\geq a_{w,1}-a_{w,2}$ for every $w\mid p$. Let $\bar{r}:G_F\to\operatorname{GL}_2({\overline{{\mathbb{F}}}_p})$ be a continuous irreducible modular representation, and let $W^?(\bar{r})$ be the set of Serre weights whose local components belong to the corresponding local predicted weight sets. The global Serre weight conjecture. For every Serre weight $a\in({\mathbb{Z}}^2_+)_0^S$, $\bar{r}$ is modular of weight $a$ if and only if $a\in W^?(\bar{r})$. This conjecture relates automorphy of $\bar{r}$ to the explicitly predicted local Serre weights; the source does not state its resolution.