Anisotropic Forms of Higher Degree Under Finite Dimensional Field Extensions |
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| Authors: | A. Johnson |
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| Affiliation: | School of Mathematical Sciences , University of Nottingham , Nottingham, UK |
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| Abstract: | Let F be a field of characteristic 0 or greater than d. We investigate anisotropic forms of degree d > 2 and their behaviour under field extensions of degree coprime to d. A form of degree d over F which permits composition or Jordan composition remains anisotropic under any field extension of degree coprime to d. Other classes of forms are constructed which stay anisotropic under such extensions. |
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| Keywords: | Anisotropic forms Forms of higher degree Homogeneous polynomials Nontrivial zeros Springer's theorem |
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