Algebras with involution that become hyperbolic over the fonction field of a conic

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We study central simple algebras with involution of the first kind that become hyperbolic over the function field of the conic associated to a given quaternion algebra $Q$. We classify these algebras in degree~4 and give an example of such a division algebra with orthogonal involution of degree~8 that does not contain $Q$ with its canonical involution, even though it contains $Q$ and is totally decomposable into a tensor product of quaternion algebras with involution.

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Rings and Algebras, 16W10; 11E04

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http://salesiana.dossiersoluciones.com/handle/123456789/212693

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0805.4138
 http://arxiv.org/abs/0805.4138

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arXiv