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Let $p$ be a prime integer and $F$ a field of characteristic $0$. Let $X$ be theof a symbol in the Galois cohomology group $H^{n+1}(F,{\mu }_p^{\otimes n})$ (for some $n\ge 1$), constructed in the proof of the Bloch-Kato conjecture. The main result of the paper affirms that the function field $F\left(X\right)$ has the following property: for any equidimensional variety $Y$, the change of field homomorphism $\mathrm{CH}\left(Y\right)\to \mathrm{CH}\left(Y_{F\left(X\right)}\right)$ of Chow groups with coefficients in integers localized at $p$ is surjective in codimensions $\<(dimX)/(p-1)$. One of the main ingredients of the proof is a computation of...