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The Mumford-Tate conjecture is a precise way of saying that the Hodge structure on singular cohomology conveys the same information as the Galois representation on $\\ell$-adic \\'{e}tale cohomology.\n  To make this precise, let $G_{\\mathrm{B}}$ be the Mumford-Tate group of the Hodge structure $H^{2}_{\\text{sing}}(A(\\mathbb{C}) \\times X(\\mathbb{C}), \\mathbb{Q})$. 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