On the unramified Brauer group of a homogeneous space

TL;DR

This paper provides a new proof that the unramified Brauer group of a homogeneous space G/H vanishes when G is a connected linear algebraic group and H is a closed connected subgroup over an algebraically closed field of characteristic zero.

Contribution

The paper introduces a novel proof of the vanishing of the unramified Brauer group for homogeneous spaces G/H under specified conditions.

Findings

Unramified Brauer group of G/H is zero.

New proof technique for the vanishing theorem.

Applicable over algebraically closed fields of characteristic zero.

Abstract

We give a new proof of the theorem stating that for any connected linear algebraic group G over an algebraically closed field k of characteristic 0 and for any closed connected subgroup H of G, the unramified Brauer group of G/H vanishes.