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Brauer groups of genus zero extensions of number fields
Authors:Jack Sonn   John Swallow
Affiliation:Department of Mathematics, Technion---Israel Institute of Technology, Haifa 32000 Israel ; Department of Mathematics, Davidson College, Box 7046, Davidson, North Carolina 28035-7046
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 $E$ of the rational numbers $mathbb{Q} $ that are split by $mathbb{Q} (sqrt{2})$, $operatorname{Br}(E)cong operatorname{Br}(mathbb{Q} (t))$.

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