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We extend the basic theory of the coniveau and strong coniveau filtrations tothe $\ell$-adic setting. By adapting the examples of Benoist--Ottem to the$\ell$-adic context, we show that the two filtrations differ over anyalgebraically closed field of characteristic not $2$.  When the base field $\mathbb{F}$ is finite, we show that the equality of thetwo filtrations over the algebraic closure $\overline{\mathbb{F}}$ has someconsequences for algebraic equivalence for codimension-$2$ cycles over$\mathbb{F}$. As an application, we prove that the third unramified cohomologygroup $H^{3}_{\text{nr}}(X,\mathbb{Q}_{\ell}/\mathbb{Z}_{\ell})$ vanishes for alarge class of rationally chain connected threefolds $X$ over $\mathbb{F}$,confirming a conjecture of Colliot-Th\'el\`ene and Kahn.

Two coniveau filtrations and algebraic equivalence over finite fields