Hodge–Tate Conditions for Landau–Ginzburg Models

Abstract

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 $\mathcal{D}$-modules of Fano manifolds and the original conjectures are explained in the appendices.