Let p be a prime integer and F a field of characteristic 0. Let X be the norm variety of a symbol in the Galois cohomology group H~(n+1)(F,μ_p~(?n)) (for some n ≥ 1), constructed in the proof of the Bloch-Kato conjecture. The main result of the paper affirms that the function field F(X) has the following property: for any equidimensional variety Y, the change of field homomorphism CH(Y) —> CH(YF(x)) 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 Chow groups of a (generalized) Rost motive (a variant of the main result not relying on this is given in the appendix). Another important ingredient is A-triviality of X, the property saying that the degree homomorphism on CHo(XL) is injective for any field extension L/F with X(L) ≠ ?. The proof involves the theory of rational correspondences reviewed in the appendix.
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