The absolute Mumford–Tate conjecture for smooth projective varieties

Let $X$ be a smooth projective variety over $K$, let $G_X^{AH}$ denote its absolute Mumford–Tate group, and let $G_{\ell,X}$ denote its $\ell$-adic algebraic Galois group. Absolute Mumford–Tate conjecture. For every smooth projective variety $X$ over $K$,

$$G_{\ell,X}=G_X^{AH}\otimes_{\mathbb{Q}}\mathbb{Q}_{\ell}.$$

This conjecture is one of the two conjectures whose conjunction implies the Mumford–Tate conjecture. Its status is not resolved in the source.