Order 5 Brauer-Manin obstructions to the integral Hasse principle on log K3 surfaces

TL;DR

This paper constructs specific log K3 surfaces to demonstrate how an order 5 Brauer-Manin obstruction can prevent the integral Hasse principle from holding, providing explicit examples and advancing understanding of obstructions in arithmetic geometry.

Contribution

It introduces explicit families of log K3 surfaces exhibiting order 5 Brauer-Manin obstructions to the integral Hasse principle, a novel contribution to the study of arithmetic obstructions.

Findings

Explicit examples of log K3 surfaces with order 5 Brauer-Manin obstructions.

Demonstration that these obstructions can prevent the integral Hasse principle.

Advancement in understanding the role of higher order Brauer-Manin obstructions.

Abstract

We construct families of log K3 surfaces and study the arithmetic of their members. We use this to produce explicit surfaces with an order 5 Brauer-Manin obstruction to the integral Hasse principle.