On PAC Extensions and Scaled Trace Forms

Details On PAC Extensions and Scaled Trace Forms On PAC Extensions and Scaled Trace Forms

2007-05-24

arxiv.org/abs/0705.3573v2

Mathematics

Number Theory

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

Scientific paper

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.

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