Scaled trace forms over number fields (Q1085194)

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.