Norm Principles for Forms of Higher Degree Permitting Composition

Abstract

Let F be a field of characteristic 0 or greater than d. Scharlau's norm principle holds for finite field extensions K over F, for certain forms ϕ of degree d over F which permit composition.

Key Words:

• Forms of higher degree
• Homogeneous polynomials
• Scharlau's norm principle
• Knebusch's norm principle

2000 Mathematics Subject Classification:

• Primary 11E76
• Secondary 11E04, 12E05

ACKNOWLEDGMENTS

The second author would like to acknowledge the support of the “Georg-Thieme-Gedächtnisstiftung” (Deutsche Forschungsgemeinschaft) during her stay at the University of Trento during the academic year 2005–2006, and thanks the Department of Mathematics at Trento for its hospitality. We thank Barquero for pointing out [2-4] to us.

Notes

Communicated by A. Prestel.