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Isotropy of Virtual Albert Forms over Function Fields of Quadrics

✍ Scribed by Oleg Izhboldin; Nikita Karpenko

Book ID
102942732
Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
563 KB
Volume
206
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let F be a field of characteristic different from 2 and let Ο• be a virtual Albert form over F, i.e., an anisotropic 6‐dimensional quadratic form over F which is still anisotropic over the field \documentclass{article}\pagestyle{empty}\begin{document}$F\left({\sqrt {d \pm \varphi } } \right).$\end{document} We give a complete description of the quadratic forms Ξ¨ such that Ο• becomes isotropic over the function field F(Ξ¨). This completes the series of works ([H6], [Lag6], [Lag], [Lee], [M2]) where the question was considered previously.

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