On PAC Extensions and Scaled Trace Forms
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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
10 pages; added results on prime-to-p extensions, removed the condition on the countability of the fields