  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.
