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Scaled trace forms over number fields. (English) Zbl 0607.10013
Let k be a field of characteristic \(\neq 2\), a scaled trace form is a quadratic form \(Q(x)=tr_{L/k}(bx^ 2)\), where L/k is a finite separable extension and \(b\in L^{\times}\). The author proves that every nondegenerate quadratic form over a hilbertian field is isometric to a scaled trace form. The proof uses a matrix characterization of scaled trace forms and Hilbert’s irreducibility theorem.
Reviewer: N.Vila

11E12 Quadratic forms over global rings and fields
12F99 Field extensions
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