Let $X$ be an algebraic variety over $\bar{\mathbb{Q}}$, then there is the l-adic cycle map $\mathrm{cl}_{et}:\mathrm{CH}^i(X)\rightarrow\mathrm{H}^{2i}(X,\mathbb{Q}_\ell(i))$ from the Chow group into the l-adic etale cohomology group, where $\mathbb{Q}_\ell(i)$ refers to the Tate twist. When $X$ is nonsingular, there is also the cycle map $\mathrm{cl}_\mathrm{C}:\mathrm{CH}^i(X)\rightarrow\mathrm{H}^{2i}(X(\mathbb{C}),\mathrm{C})$ into the Singular cohomology group. I wonder what the relation or compatibility between these two cycle maps is? (Is there a reference on this question?)

In Milne's lecture notes on Etale cohomology, he states a comparison theorem (Thm. 21.1) between etale cohomology and the cohomology based on complex topology. According to it, there is a canonical isomorphism $\mathrm{H}^{2i}(X,\mathrm{Z}/n\mathrm{Z})\cong \mathrm{H}^{2i}(X(\mathbb{C}),\mathrm{Z}/n\mathrm{Z})$. But I don't know how to go further to do the comparison of the cycle maps.