Algebraic and analytic Brauer groups of homogeneous spaces

TL;DR

This paper computes the algebraic and analytic Brauer groups of homogeneous spaces under certain complex algebraic groups, providing insights into their structure and properties.

Contribution

It offers a novel computation of both algebraic and analytic Brauer groups for a class of homogeneous spaces with connected stabilizers.

Findings

Explicit formulas for algebraic Brauer groups.

Explicit formulas for analytic Brauer groups.

Comparison between algebraic and analytic Brauer groups.

Abstract

In this article, we compute both the algebraic and the analytic Brauer groups of a homogeneous space under the action of a connected, simply connected, semisimple complex algebraic group, where the stabilizer subgroup is closed and connected.