Frobenius map on local Calabi-Yau manifolds

TL;DR

This paper investigates the Frobenius action on the p-adic cohomology of specific non-compact Calabi-Yau threefolds and relates it to the cohomology of associated curves, providing new insights into their arithmetic properties.

Contribution

It establishes a connection between the Frobenius actions on Calabi-Yau threefolds and their associated curves, and offers an interpretation of the Griffiths-Dwork method.

Findings

Frobenius action on Calabi-Yau threefolds is related to that on associated curves

Provides a new perspective on p-adic cohomology for non-compact Calabi-Yau manifolds

Includes an interpretation of the Griffiths-Dwork method

Abstract

We prove results that, for a certain class of non-compact Calabi-Yau threefolds, relate the Frobenius action on their $p$-adic cohomology to the Frobenius action on the $p$-adic cohomology of the corresponding curves. In the appendix, we describe our interpretation of the Griffiths-Dwork method.