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

Karim Johannes Becher (1) , Nicolas Grenier-Boley (2) , Jean-Pierre Tignol (3)

1 Universiteit Antwerpen = University of Antwerpen [Antwerpen]
2 LDAR (EA_4434) - Laboratoire de Didactique André Revuz
3 Département de mathématique [Louvain]

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.

Mots clés: Witt index; corestriction; Albert form; charac-; teristic two; isotropy

Domaines: Anneaux et algèbres [math.RA]

Karim Johannes Becher, Nicolas Grenier-Boley, Jean-Pierre Tignol. Transfer of quadratic forms and of quaternion algebras over quadratic field extensions. Archiv der Mathematik, 2018, 111 (2), pp.135-143. ⟨10.1007/s00013-018-1198-5⟩. ⟨hal-01853557⟩