Fields for which the projective Schur subgroup is the whole Brauer group
The authors prove that if \(K\) is a finitely generated infinite field, then the Brauer group of \(K\) equals the projective Schur subgroup of \(K\) if and only if \(K\) is a global field. Moreover, if \(K( (t))\) is the field of formal power series in \(t\) over \(K\) (again a finitely generated infinite field), then the Brauer group of \(K( (t))\) equals the projective Schur subgroup of \(K( (t))\) if and only if \(K=\mathbb{Q}\).
scientific article; zbMATH DE number 1850619
scientific article