Cohomological Friedlander–Mazur conjecture

Let $X$ be a smooth projective variety, and let $T^pH^l(X;\Q)$ be the topological filtration defined using the natural transformation from morphic cohomology to singular cohomology. Let $N^pH^l(X;\Q)$ be the arithmetic, or coniveau, filtration. Cohomological Friedlander–Mazur conjecture. For all nonnegative integers $l,p$,

$$T^{l-p}H^l(X;\Q)=N^pH^l(X;\Q).$$

This is the cohomological reformulation of the Friedlander–Mazur equality of topological and geometric filtrations. The source explains that the inclusion $T^{l-p}H^l(X;\Q)\subset N^pH^l(X;\Q)$ is known, while equality remains conjectural.