Coherence of group algebras of surface-by-cyclic groups

Let $\Sigma$ be a closed surface, let $\psi\in\operatorname{Out}(\pi_1(\Sigma))$, and let

$$G\cong \pi_1(\Sigma)\rtimes_{\psi}\mathbb{Z}.$$

Surface-by-cyclic group-algebra coherence conjecture. The group algebra $\mathbb{Q}[G]$ is coherent. The source identifies the virtual surface-group case as difficult and open, motivating this conjectural extension of coherence results for hyperbolic-by-cyclic groups.