English

$p$-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 pp-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}
}
R2 v1 2026-06-22T05:58:56.628Z