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Transfer of quadratic forms and of quaternion algebras over quadratic field extensions |
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| Authors: | Karim Johannes Becher Nicolas Grenier-Boley Jean-Pierre Tignol |
| Affiliation: | 1.Departement Wiskunde en Informatica,Universiteit Antwerpen,Antwerpen,Belgium;2.LDAR (EA4434), UA, UCP, UPD, UPEC, URN, Université de Rouen Normandie,Mont-Saint-Aignan,France;3.ICTEAM Institute,Université Catholique de Louvain,Louvain-la-Neuve,Belgium |
| Abstract: | Two different proofs are given showing that a quaternion algebra Q defined over a quadratic étale extension K of a given field has a corestriction that is not a division algebra if and only if Q contains a quadratic algebra that is linearly disjoint from K. This is known in the case of a quadratic field extension in characteristic different from two. In the case where K is split, the statement recovers a well-known result on biquaternion algebras due to Albert and Draxl. |
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