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Isotropy of Virtual Albert Forms over Function Fields of Quadrics
Author(s) -
Izhboldin Oleg,
Karpenko Nikita
Publication year - 1999
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19992060104
Subject(s) - isotropy , mathematics , anisotropy , quadratic equation , field (mathematics) , function (biology) , function field , quadratic form (statistics) , series (stratigraphy) , quadratic function , combinatorics , mathematical physics , pure mathematics , mathematical analysis , geometry , physics , quantum mechanics , paleontology , evolutionary biology , biology
Let F be a field of characteristic different from 2 and let ϕ 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 Ψ such that ϕ becomes isotropic over the function field F(Ψ). This completes the series of works ([H6], [Lag6], [Lag], [Lee], [M2]) where the question was considered previously.