Serre's conjecture relating the Mumford–Tate and motivic Mumford–Tate groups

Let $M$ be a motive in the relevant motivic category, with rational polarized Hodge realization $(V,\psi)$. Let $\operatorname{MMT}_{\sim}(M)$ be its motivic Mumford–Tate group. Serre's conjecture.

$$\operatorname{MT}(V,\psi)=\operatorname{MMT}_{\sim}(M)^{\circ}.$$

The paper notes that this is known for motives associated with abelian varieties in the category of absolute Hodge cycles and for AHC motives, but it is not established for arbitrary motives and equivalence relations.