Variation of the unit roots along the Dwork family of Calabi-Yau varieties

TL;DR

This paper investigates how unit roots vary in Dwork families of Calabi-Yau varieties over finite fields, providing a p-adic formula for these roots away from the Hasse locus using Dwork-Katz methods and formal group laws.

Contribution

It introduces a p-adic analytic formula for unit roots in Dwork families, enhancing understanding of their variation over finite fields.

Findings

Derived a p-adic formula for unit roots away from the Hasse locus.

Analyzed the variation of unit roots using Dwork-Katz method.

Connected the variation to formal group laws.

Abstract

We study the variation of unit roots of the Dwork families of Calabi-Yau varieties over a finite field by the method of Dwork-Katz and also from the point of view of formal group laws. A p-adic analytic formula for the unit roots away from the Hasse locus is obtained.