Hodge-Tate Conditions for Landau-Ginzburg Models.

We give a sufficient condition for a class of tame compactified Landau-Ginzburg models in the sense of Katzarkov-Kontsevich-Pantev to satisfy some versions of their conjectures. We also give examples that satisfy the condition. The relations to the quantum D-modules of Fano manifolds and the original conjectures are explained in the appendices. [ABSTRACT FROM AUTHOR]