Differential forms and Brauer classes in positive characteristic

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.