Advances in Theoretical and Mathematical Physics
Volume 19 (2015)
$p$-adic Berglund–Hübsch duality
Pages: 1115 – 1139
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.