Beilinson–Bloch conjecture over global fields

Let $K$ be a global field, let $Y$ be a smooth projective variety over $K$, and let $i\in\mathbb{Z}$. Write $\operatorname{CH}^i(Y)_0$ for the kernel of the cycle class map and let $L(H^{2i-1}(\overline{Y},\mathbb{Q}_{\ell}),s)$ denote the associated $L$-function. Beilinson–Bloch conjecture.

$$\dim_{\mathbb{Q}}\operatorname{CH}^i(Y)_0=\operatorname*{ord}_{s=i}L(H^{2i-1}(\overline{Y},\mathbb{Q}_{\ell}),s).$$

This is the paper's recalled formulation over global fields and is a restatement of Candidate 3, so the two statements should be merged into one database row.