Voisin–Pura Bloch–Beilinson filtration conjecture modulo algebraic equivalence

Let $Y$ be a smooth projective variety and let $F$ be a Bloch–Beilinson filtration with rational coefficients on its Chow groups. Assume that $F$ also induces a filtration on Chow groups modulo algebraic equivalence. Voisin–Pura's conjecture. For every $k$, the $k$-th Chow group modulo algebraic equivalence has trivial $k$-th filtration step:

$$F^k\operatorname{CH}^k(Y)/\operatorname{alg}=0.$$

The conjecture generalizes Nori's conjecture on $\operatorname{CH}^2$. It strengthens the expected property $F^{k+1}\operatorname{CH}^k(Y)_\mathbb{Q}=0$ and is presented as an open conjecture whose consequences include restrictions on infinitesimal invariants.