Brauer groups and étale homotopy type

Abstract

AbstractExtending a result of Schröer on a Grothendieck question in the context of complex analytic spaces, we prove that the surjectivity of the Brauer map for schemes depends on their étale homotopy type. We use properties of algebraic spaces to apply this to some classes of proper and smooth algebraic schemes. In particular, we recover a result of Hoobler and Berkovich for abelian varieties.