Beilinson–Soulé vanishing conjecture in weight zero

Let $F$ be a field, and let $K^{(q)}_{2q}(F)$ and $\operatorname{CH}^q(\operatorname{Spec}F,2q)$ have the meanings used in the Beilinson–Soulé vanishing conjecture. Beilinson–Soulé vanishing conjecture. For $q>0$,

$$K^{(q)}_{2q}(F)\simeq \operatorname{CH}^q(\operatorname{Spec}F,2q)=0.$$

This is the special case $p=0$ of the preceding Beilinson–Soulé vanishing conjecture and is assumed in the paper's argument; no resolution status is supplied.