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Trace forms of Galois extensions in the presence of a fourth root of unity

J. Minac·Z. Reichstein
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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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J. Minac, Z. Reichstein. 2003-09-05. Trace forms of Galois extensions in the presence of a fourth root of unity. https://arxiv.org/abs/math/0309104

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