Excellence of function fields of conics

Merkurjev, Alexander;Tignol, Jean-Pierre
(2016) L’Enseignement Mathématique — Vol. 62, n° 3-4, p. 421-456 (2016)

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  • Merkurjev, AlexanderUniversity of California, Los Angeles
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  • Tignol, Jean-Pierreorcid-logoUCLouvain
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Abstract
For every generalized quadratic form or hermitian form over a division algebra, the anisotropic kernel of the form obtained by scalar extension to the function field of a smooth projective conic is defined over the field of constants. The proof does not require any hypothesis on the characteristic.
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Merkurjev, A., & Tignol, J.-P. (2016). Excellence of function fields of conics. L’Enseignement Mathématique, 62(3-4), 421-456. https://doi.org/10.4171/LEM/62-3/4-3 (Original work published 2016)