Hodge–Tate conditions for Landau–Ginzburg models

In the context of mirror symmetry for Fano manifolds, Katzarkov–Kontsevich–Pantev proposed some conjectures for Landau–Ginzburg models. In this talk, I will give a sufficient condition for Landau–Ginzburg models to satisfy some versions of their conjectures. This condition is called Hodge–Tate condition and can be checked for some examples of Landau–Ginzburg models. I will also explain that this condition is natural in the context of mirror symmetry.