Bloch–Beilinson Abel–Jacobi injectivity conjecture for higher Chow groups

Let $W$ be a smooth projective variety over $\overline{\mathbb{Q}}$, and let $r$ and $m$ be integers for which the displayed higher Chow group is defined. Let

$$\operatorname{CH}^r_{\mathrm{hom}}(W/\overline{\mathbb{Q}},m;\mathbb{Q})\longrightarrow J\big(H^{2r-m-1}(W,\mathbb{Q}(r))\big)$$

be the generalized Abel–Jacobi map. Generalized Bloch–Beilinson conjecture. This map is injective. The source presents this as the higher-Chow analogue of the Bloch–Beilinson conjecture, under the Hodge conjecture together with a generalized BBC; no resolution status is given.