$p$-adic Berglund-Hübsch Duality

Abstract

Berglund-Hübsch duality is an example of mirror symmetry between orbifold Landau-Ginzburg models. In this paper we study a D-module-theoretic variant of Borisov's proof of Berglund-Hübsch duality. In the $p$-adic case, the D-module approach makes it possible to endow the orbifold chiral rings with the action of a non-trivial Frobenius endomorphism. Our main result is that the Frobenius endomorphism commutes with Berglund-Hübsch duality up to an explicit diagonal operator.

References in corpus (3)

• A Generalized Construction of Mirror Manifolds
• FJRW rings and Landau-Ginzburg Mirror Symmetry
• The Mirror Map for Invertible LG Models