Transfer of quadratic forms and of quaternion algebras over quadratic field extensions

Abstract : Two different proofs are given showing that a quaternion algebra defined over a quadraticétalequadraticétale extension of a given field has trivial corestriction if and only if it is extended from a quaternion algebra over the base field of the extension. This is well-known in the case of a quadratic field extension in characteristic different from two. In the case of a split quadraticétalequadraticétale extension the statement recovers a well-known result on biquaternion algebras due to Albert and Draxl.
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Karim Becher, Nicolas Grenier-Boley, Jean-Pierre Tignol. Transfer of quadratic forms and of quaternion algebras over quadratic field extensions. Archiv der Mathematik, Springer Verlag, 2018, 111 (2), pp.135-143. ⟨10.1007/s00013-018-1198-5⟩. ⟨hal-01853557⟩

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