Anisotropic Forms of Higher Degree Under Finite Dimensional Field Extensions |
| |
| Authors: | A Johnson |
| |
| Institution: | School of Mathematical Sciences , University of Nottingham , Nottingham, UK |
| |
| 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. |
| |
| Keywords: | Anisotropic forms Forms of higher degree Homogeneous polynomials Nontrivial zeros Springer's theorem |
|
