Anisotropic Forms of Higher Degree Under Finite Dimensional Field Extensions

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.

Key Words:

• Anisotropic forms
• Forms of higher degree
• Homogeneous polynomials
• Nontrivial zeros
• Springer's theorem

2000 Mathematics Subject Classification:

• Primary 11E76
• Secondary 11E04, 12E05

Notes

Communicated by S. Sehgal.