Motivic weight zero on all qcqs schemes

PDF p. 4: Property (1)

Assume the Axiom of Choice and fixed compatible site and universe size bounds for the constructions below. Let $X$ be any qcqs $k$-scheme and let $F$ be the prime subfield of $k$. For $R{\mathrm{\Gamma }}_{\mathrm{c}\mathrm{d}\mathrm{h}}(X,\mathbb{Z})$ use the ordinary constant integer sheaf on the general qcqs $F$-scheme cdh site specified by the preceding qcqs-site construction, evaluated at the underlying $F$-scheme $X$. Then there is a natural equivalence $\mathbb{Z}(0{)}_{\mathrm{m}\mathrm{o}\mathrm{t}}(X)\simeq R{\mathrm{\Gamma }}_{\mathrm{c}\mathrm{d}\mathrm{h}}(X,\mathbb{Z}),$ and natural isomorphisms $H_{\mathrm{m}\mathrm{o}\mathrm{t}}^{i,0}(X,\mathbb{Z})\cong H_{\mathrm{c}\mathrm{d}\mathrm{h}}^i(X,\mathbb{Z})$ for all integers $i$. Negative-degree groups vanish. The site convention is part of this statement and covers every qcqs $X\mathrm{/}k$.

The source qcqs cdh site