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 which satisfy the condition. The relations to the quantum D-modules of Fano manifolds and the original conjectures are explained in Appendices.