Bloch–Beilinson Abel–Jacobi injectivity conjecture

Let $W$ be a smooth projective variety over $\overline{\mathbb{Q}}$, and let $r\geq 0$ be an integer. Let $J(H^{2r-1}(W(\mathbb{C}),\mathbb{Q}(r)))$ denote the relevant intermediate Jacobian, and let

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

be the Abel–Jacobi map. Bloch–Beilinson Abel–Jacobi conjecture. This map is injective. This conjecture is attributed in the source to Beilinson and Bloch; its resolution status is not specified.