Ramakrishnan's injectivity conjecture for the Bloch regulator

Let $F$ be a subfield of $\mathbb{C}$ with embedding $\sigma:F\hookrightarrow\mathbb{C}$. Let $\mathcal B(F)$ and $\mathcal B(\mathbb{C})$ denote the corresponding Bloch groups, and let $\mathbb{Q}(2)=(2\pi\sqrt{-1})^2\mathbb{Q}\subset\mathbb{C}$. Ramakrishnan's conjecture. For every such embedded subfield, the map

$$\mathcal B(F)\otimes\mathbb{Q}\stackrel{\sigma}{\longrightarrow}\mathcal B(\mathbb{C})\otimes\mathbb{Q}\longrightarrow\mathbb{C}/\mathbb{Q}(2)$$

is injective. This generalizes Milnor's conjecture and is related to injectivity of the Bloch regulator; the source gives no resolution evidence, so the conjecture is recorded as open.