3 problems

Quantum Galois group conjecture. If $q$ is not a root of unity, the injection in Proposition 6.8o is an equality, so

Equality conjecture. If $q$ is not a root of unity, the injection $\mathcal{F}_{L/k}(A)\rightarrow\widehat{G}_{III}$ is an equality.

Equality conjecture. If $q$ is not a root of unity, the inclusion $\mathcal{NCF}_{L/k}(A)\hookrightarrow\widehat{G}_{II}(A)$ is an equality.