Invertible Calabi-Yau Orbifolds over Finite Fields II

TL;DR

This paper proposes a conjecture about the zeta function of certain Calabi-Yau orbifolds over finite fields, providing evidence and connecting it to cohomology theories and Weil conjectures.

Contribution

It introduces a new conjecture on the zeta functions of crepant resolutions of Berglund--Hübsch orbifold hypersurfaces and explores its mathematical properties.

Findings

Conjectural zeta function satisfies Weil conjectures.

Provides numerical evidence supporting the conjecture.

Connects the zeta function with Monsky--Washnitzer cohomology.

Abstract

We state a conjecture about the zeta function of crepant resolutions of Berglund--H\"ubsch orbifold hypersurfaces over a finite field. In addition to numerical evidence, we show that our conjectural zeta function satisfies the Weil conjectures and we elucidate its connection with Monsky--Washnitzer cohomology.