The motivic Mumford–Tate conjecture

Let $M$ be a motive in the chosen motivic category, let $G_{l,K}^{\operatorname{alg}}$ be the algebraic group attached to its $l$-adic realization, and let $\operatorname{MMT}_{\sim}(M)$ be its motivic Mumford–Tate group. Motivic Mumford–Tate conjecture. For any prime number $l$,

$$G_{l,K}^{\operatorname{alg}}=\operatorname{MMT}_{\sim}(M)_{\mathbb Q_l}.$$

This is the motivic analogue of the Mumford–Tate conjecture and is open in general.