Standard conjecture on the perfectness of algebraic cohomology pairings

Let $X_s$ be the special fiber, and let $A^*(X_s)$ and $A_*(X_s)$ be the images of the cohomological and homological cycle class maps introduced in the paper. Their intersection pairing is

$$A^*(X_s)\times A_*(X_s)\longrightarrow\mathbb Q.$$

Perfectness conjecture. The intersection pairing on algebraic cohomology classes is perfect. This is presented as one of the paper's analogues of Grothendieck's standard conjectures, and the supplied text gives no resolution status.