The weak rationality conjecture for abelian varieties

Let $A$ be an abelian variety over $\mathbb{Q}^{\mathrm{al}}$ with good reduction at $w$, and let $\gamma$ be a Hodge class on $A$. Call $\gamma$ $w$-Lefschetz if its specialization $\gamma_{0}$ is Lefschetz, and weakly $w$-Lefschetz if $\gamma_{0}$ is weakly Lefschetz. The weak rationality conjecture. Every weakly $w$-Lefschetz class is $w$-Lefschetz. This asserts that the rational and adelic conditions on the specialization of a Hodge class agree; the source presents it as the weak rationality conjecture, with no resolution stated.