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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

##### MSC:
 11E12 Quadratic forms over global rings and fields 12F99 Field extensions
##### Keywords:
scaled trace form; quadratic form; hilbertian field
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##### References:
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