4 problems

Let $M=H^w(X)$ arise from a smooth projective variety $X$ over a number field $F$, and fix an embedding $\sigma:F\hookrightarrow\mathbb C$. Let $G_{MT}$ be the Mumford–Tate group o…

Let $M$ be a motive over a number field $F$ with Betti realization $M_B$, Mumford–Tate group $G_{MT}$, and adelic Galois representation … Assume that the Betti realization $M_B$ is…

Let $X$ be as above, let $H$ be the Mumford–Tate group, and let $H^{\operatorname{sc}}$ be the simply connected cover of its derived group. Let…

Let $E$ be a motive over $K$, and let $G_{\mathcal{M}(E)}$ be its motivic Galois group. Assume that $G_{\mathcal{M}(E)}$ is connected, and let … be the adelic Galois representation…