Brauer groups of genus zero extensions of number fields

Abstract

We determine the isomorphism class of the Brauer groups of certain nonrational genus zero extensions of number fields. In particular, for all genus zero extensions E E of the rational numbers Q \mathbb {Q} that are split by Q ( 2 ) \mathbb {Q}(\sqrt {2}) , Br ⁡ ( E ) ≅ Br ⁡ ( Q ( t ) ) \operatorname {Br}(E)\cong \operatorname {Br}(\mathbb {Q}(t)) .