I wonder whether the "finite coefficient version" of Beilinson-Soule conjecture i.e. the following statement holds or not.

STATEMENT:

Let $X$ be a smooth and projective scheme over a finite field $\mathbb{F}_{p}$.

Then, Bloch's higher chow group $CH_{0}(X,i,\mathbb{Z}/n)$ vanishes for $n$ satisfying (n,p) =1 and $i>2dim(X)$.

Please give me any advice.