In 1968, Grothendieck proposed a family of conjectures concerning algebraic cycles called the Standard Conjectures. The conjectures have been proven in some special cases, but they remain wide open in general. In 2011, Marcolli-Tabuada realized two of these conjectures as special cases of more general conjectures, involving differential graded categories, which they call Noncommutative Standard Conjectures C and D. The goal of this talk is to discuss a proof, joint with Mark Walker, of Noncommutative Standard Conjecture D in a special case which does not fall under the purview of Grothendieck's original conjectures: namely, in the setting of matrix factorizations.