J. Minac, Z. Reichstein, Trace forms of Galois extensions in the presence of a 4th root of unity, International Math. Research Notices, 8 (2004) 389-410.

Abstract: We study quadratic forms that can occur as trace forms of Galois field extensions L/K, under the assumption that K contains a primitive 4th root of unity. M. Epkenhans conjectured that any such form is a scaled Pfister form. We prove this conjecture and classify the finite groups G which admit a G-Galois extension L/K with a non-hyperbolic trace form. We also give several applications of these results.

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