In communication complexity, the log-rank conjecture states that
$$cc(M) = (\log rk(M))^{O(1)}$$
Where $cc(M)$ is the communication complexity of $M(x,y)$ and $rk(M)$ is the rank of $M$ (as a matrix) over the reals.
However, when you are just using the rank-method to lower bound $cc(M)$ you can use $rk$ over any field that is convenient. Why does the log-rank conjecture restrict to rk over the reals? Is the conjecture resolved for $rk$ over fields of non-zero characteristic? If not, is it of interest or is there something special about $rk$ over $\mathbb{R}$?