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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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