Non-degeneracy of Cohomological Traces for General Landau–Ginzburg Models

We prove non-degeneracy of the cohomological bulk and boundary traces for general open-closed Landau-Ginzburg models associated to a pair $(X,W)$, where $X$ is non-compact complex manifold with trivial canonical line bundle $W$ complex-valued holomorphic function defined on $X$, assuming only that critical locus compact (but may not consist isolated points). These results can be viewed as certain "deformed" versions Serre duality. The first amounts duality property hypercohomology sheaf Koszul $W$, while second equivalent statement power shift functor even subcategory $\mathbb{Z}_2$-graded category topological D-branes such models.