General Hodge conjecture

Let $X$ be a smooth projective complex scheme, let $l\ge1$ and $p\ge0$, and define the coniveau filtration by

$$F^p_aH^l(X,\mathbb Q)=\bigcup_{\operatorname{codim}_X(Y)\ge p}\ker\bigl(H^l(X,\mathbb Q)\to H^l(X-Y,\mathbb Q)\bigr).$$

Here $F^pH^l(X,\mathbb C)$ is the Hodge filtration. General Hodge conjecture. $F^p_aH^l(X,\mathbb Q)$ is the largest sub-Hodge structure of

$$F^pH^l(X,\mathbb C)\cap H^l(X,\mathbb Q).$$

The source presents this as the general Hodge conjecture and gives no resolution status for the asserted statement.