Marcolli–Tabuada's noncommutative Standard Conjecture D

Assume that $k$ is a field of characteristic $0$, and let $\mathcal{C}$ be a smooth and proper differential $\mathbb{Z}$-graded category over $k$. Classes in $K_0(\mathcal{C})_{\mathbb{Q}}$ are homologically equivalent when they have the same image under the Chern character map to periodic cyclic homology, and numerically equivalent when they induce the same Euler pairing.

Marcolli–Tabuada's noncommutative Standard Conjecture D. If $\mathcal{C}$ is a smooth and proper differential $\mathbb{Z}$-graded category over a field $k$ of characteristic $0$, homological and numerical equivalence coincide for $\mathcal{C}$.

This is the noncommutative analogue of Grothendieck's Standard Conjecture D. The paper proves the $\mathbb{Z}/2$-graded analogue for categories of matrix factorizations associated to isolated hypersurface singularities over fields of characteristic $0$.