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

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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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Authors and Affiliations

  1. Departement Wiskunde en Informatica, Universiteit Antwerpen, Middelheimlaan 1, 2020, Antwerpen, Belgium

    Karim Johannes Becher

  2. LDAR (EA4434), UA, UCP, UPD, UPEC, URN, Université de Rouen Normandie, Mont-Saint-Aignan, France

    Nicolas Grenier-Boley

  3. ICTEAM Institute, Université Catholique de Louvain, Avenue G. Lemaître 4, Box L4.05.01, 1348, Louvain-la-Neuve, Belgium

    Jean-Pierre Tignol

Authors
  1. Karim Johannes Becher
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  2. Nicolas Grenier-Boley
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  3. Jean-Pierre Tignol
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Corresponding author

Correspondence to Jean-Pierre Tignol.

Additional information

Karim Johannes Becher was supported by the FWO Odysseus Programme (project Explicit Methods in Quadratic Form Theory), funded by the Fonds Wetenschappelijk Onderzoek – Vlaanderen. Jean-Pierre Tignol acknowledges support from the Fonds de la Recherche Scientifique–FNRS under Grants Nos. J.0014.15 and J.0149.17.

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Becher, K.J., Grenier-Boley, N. & Tignol, JP. Transfer of quadratic forms and of quaternion algebras over quadratic field extensions. Arch. Math. 111, 135–143 (2018). https://doi.org/10.1007/s00013-018-1198-5

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  • DOI: https://doi.org/10.1007/s00013-018-1198-5

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