Equivariant derived equivalence and rational points on K3 surfaces

TL;DR

This paper investigates the arithmetic properties of K3 surfaces that are derived equivalent over Laurent power series fields, utilizing equivariant geometry and cyclic group actions to understand their rational points.

Contribution

It introduces a novel approach connecting derived equivalence and equivariant geometry to study rational points on K3 surfaces.

Findings

Derived equivalent K3 surfaces exhibit specific arithmetic behaviors.

Equivariant geometry provides new insights into rational points on K3 surfaces.

Cyclic group actions influence the arithmetic properties of these surfaces.

Abstract

We study arithmetic properties of derived equivalent K3 surfaces over the field of Laurent power series, using the equivariant geometry of K3 surfaces with cyclic groups actions.