Differential forms and Brauer classes in positive characteristic

TL;DR

This paper explores the relationship between differential forms and p-torsion Brauer classes in positive characteristic, focusing on supersingular K3 surfaces and their impact on the Brauer-Manin obstruction.

Contribution

It introduces a new construction linking differential forms to Brauer classes in positive characteristic and analyzes their role in the Brauer-Manin obstruction for supersingular K3 surfaces.

Findings

p-torsion Brauer classes from differential forms are related to supersingular K3 surfaces.

These classes contribute to the Brauer-Manin obstruction on certain varieties.

The study provides insights into the Brauer-Manin set for supersingular K3 surfaces.

Abstract

We study $p$-torsion Brauer classes in positive characteristic arising from differential forms. We relate this construction to the Brauer group of supersingular K3 surfaces and analyze the contribution of these classes to the Brauer-Manin obstruction. As an application, we examine the Brauer-Manin set of supersingular K3 surfaces and of varieties admitting many differential forms.