$p$-adic Berglund-H\"ubsch Duality
Mathematical Physics
2024-02-23 v2 Algebraic Geometry
math.MP
Number Theory
Abstract
Berglund-H\"ubsch 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-H\"ubsch duality. In the -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-H\"ubsch duality up to an explicit diagonal operator.
Cite
@article{arxiv.1409.5017,
title = {$p$-adic Berglund-H\"ubsch Duality},
author = {Marco Aldi and Andrija Peruničić},
journal= {arXiv preprint arXiv:1409.5017},
year = {2024}
}