Karim Johannes Becher, Nicolas Grenier-Boley, Jean-Pierre Tignol: Transfer of quadratic forms and of quaternion algebras over quadratic field extensions


Submission: 2016, Oct 21

A theorem of Albert-Draxl states that if a tensor product of two quaternion division algebras Q1, Q2 over a field F is not a division algebra, then there exists a separable quadratic extension of F that embeds as a subfield in Q1 and in Q2. We establish a modified version of this result where the tensor product of quaternion algebras is replaced by the corestriction of a single quaternion algebra over a separable field extension. As a tool in the proof, we show that if the transfer of a nonsingular quadratic form \phi over a quadratic extension is isotropic for a linear functional s such that s(1)=0, then \phi contains a nondegenerate subform defined over the base field.

2010 Mathematics Subject Classification: 11E81, 11E04, 16K20, 16H05

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