  We study the conjecture claiming that, over a flexible field, isotropic Chow
groups coincide with numerical Chow groups (with ${\Bbb{F}}_p$-coefficients).
This conjecture is essential for understanding the structure of the isotropic
motivic category and that of the tensor triangulated spectrum of Voevodsky
category of motives. We prove the conjecture for the new range of cases. In
particular, we show that, for a given variety $X$, it holds for sufficiently
large primes $p$. We also prove the $p$-adic analogue. This permits to
interpret integral numerically trivial classes in $CH(X)$ as
$p^{\infty}$-anisotropic ones.
