Abstract
Let f(X) and g(Y) be nondegenerate quadratic forms of dimensions m and n, respectively, over K, char K ≠ 2. The problem of birational composition of f(X) and g(Y) is considered: When is the product f(X) · g(Y) birationally equivalent over K to a quadratic form h(Z) over K of dimension m + n? The solution of the birational composition problem for anisotropic quadratic forms over K in the case of m = n = 2 is given. The main result of the paper is the complete solution of the birational composition problem for forms f(X) and g(Y) over a local field P, char P ≠ 2.
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Original Russian Text © A. A. Bondarenko, 2009, published in Matematicheskie Zametki, 2009, Vol. 85, No. 5, pp. 661–670.
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Bondarenko, A.A. Birational composition of quadratic forms over a local field. Math Notes 85, 638–646 (2009). https://doi.org/10.1134/S0001434609050046
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DOI: https://doi.org/10.1134/S0001434609050046