Zeta-functions of certain K3 fibered Calabi--Yau threefolds

TL;DR

This paper investigates the arithmetic properties and zeta-functions of certain K3-fibered Calabi--Yau threefolds, focusing on their deformations and variations using p-adic cohomology.

Contribution

It provides a detailed study of the zeta-functions of specific Calabi--Yau threefolds constructed via twist maps, including their deformation behavior.

Findings

Computed zeta-functions for the class of Calabi--Yau threefolds.

Analyzed the variation of zeta-functions under deformations.

Applied p-adic rigid cohomology to study arithmetic properties.

Abstract

We consider certain $K3$-fibered Calabi--Yau threefolds. One class of such Calabi--Yau threefolds are constructed by Hunt and Schimmrigk using twist maps. They are realized in weighted projective spaces as orbifolds of hypersurfaces. Our main goal of this paper is to investigate arithmetic properties of these Calabi--Yau threefolds. We also consider deformations of our Calabi--Yau threefolds, and we study the variation of the zeta-functions using $p$-adic rigid cohomology theory.