Merkurjev–Suslin conjecture on the reduced norm in $K_{2}$

Let $F$ be a local or global field, and let $A$ be a finite-dimensional central simple $F$-algebra. Let $A_v$ denote the algebra obtained at a place $v$ of $F$, and let the direct sum range over the real places for which $A_v$ is non-split.

Merkurjev–Suslin conjecture. There is an exact sequence

$$0\longrightarrow K_{2}(A)\overset{\operatorname{nr}}{\longrightarrow}K_{2}(F)\longrightarrow\bigoplus_{v}\mathbb{Z}/2\mathbb{Z}\longrightarrow0.$$

If $F$ is a $p$-adic or complex local field, the indexing set is empty. The source identifies this as an old conjecture of Merkurjev and Suslin and states that it remains open; the asserted sequence is intended to describe the obstruction to surjectivity of the reduced norm at the relevant real places.