paper

On PAC Extensions and Scaled Trace Forms

arXiv:0705.3573

Abstract

Any non-degenerate quadratic form over a Hilbertian field (e.g., a number field) is isomorphic to a scaled trace form. In this work we extend this result to more general fields. In particular, prosolvable and prime-to-p extensions of a Hilbertian field. The proofs are based on the theory of PAC extensions.

10 pages; added results on prime-to-p extensions, removed the condition on the countability of the fields

On PAC Extensions and Scaled Trace Forms · wovepaper