Hodge-Tate conditions for Landau-Ginzburg models

TL;DR

This paper establishes a sufficient condition under which certain Landau-Ginzburg models meet specific conjectures, providing examples and exploring connections to quantum D-modules of Fano manifolds.

Contribution

It introduces a new sufficient condition for Landau-Ginzburg models to satisfy conjectures and illustrates this with concrete examples.

Findings

Identified a sufficient condition for Landau-Ginzburg models to meet conjectures

Provided explicit examples satisfying the condition

Explored relations to quantum D-modules of Fano manifolds

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.