Colliot-Thélène–Parimala–Suresh local-global conjecture for projective homogeneous spaces

Let $F$ be the function field of a $p$-adic curve, let $G$ be a connected linear algebraic group over $F$, and let $Z$ be a projective homogeneous space under $G$. Colliot-Thélène–Parimala–Suresh's local-global conjecture. The variety $Z$ satisfies the local-global principle with respect to the set $\Omega_F$ of divisorial discrete valuations of $F$; that is, $Z(F)\neq\emptyset$ if and only if $Z(F_\nu)\neq\emptyset$ for every $\nu\in\Omega_F$. This conjecture concerns the existence of rational points on projective homogeneous spaces over function fields of $p$-adic curves and is presented as a conjecture of Colliot-Thélène, Parimala, and Suresh; the source does not state whether it has been resolved.