Sums of Squares of Linear Forms
نویسندگان
چکیده
Let k be a real field. We show that every non-negative homogeneous quadratic polynomial f(x1, . . . , xn) with coefficients in the polynomial ring k[t] is a sum of 2n · τ(k) squares of linear forms, where τ(k) is the supremum of the levels of the finite non-real field extensions of k. From this result we deduce bounds for the Pythagoras numbers of affine curves over fields, and of excellent two-dimensional local henselian rings.
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تاریخ انتشار 2006