Colliot-Thélène–Kahn conjecture on unramified cohomology of uniruled threefolds

Let $\mathbb{F}$ be the finite field under consideration, let $\ell$ be a prime, and let $X$ be a smooth projective geometrically uniruled $\mathbb{F}$-variety of dimension $3$. The group $H^{3}_{\operatorname{nr}}(X,\mathbb{Q}_{\ell}/\mathbb{Z}_{\ell}(2))$ is the third unramified cohomology group of $X$ with these coefficients. Colliot-Thélène–Kahn conjecture. For every such $X$,

$$H^{3}_{\operatorname{nr}}(X,\mathbb{Q}_{\ell}/\mathbb{Z}_{\ell}(2))=0.$$

This predicts the vanishing of a stable birational invariant for geometrically uniruled threefolds over finite fields and is presented as a conjecture of Colliot-Thélène and Kahn; its resolution status is not specified in the supplied text.