Triangulated categories of singularities and equivalences between Landau-Ginzburg models

The existence of a certain type of equivalence between triangulated categories of singularities for varieties of different dimensions is proved. This class of equivalences generalizes the so-called Knoerrer periodicity. As a consequence, equivalences between the categories of D-branes of type B on Landau-Ginzburg models of different dimensions are obtained.