Jan Minac & Zinovy Reichstein: Trace forms of Galois extensions in the presence of a fourth root of unity

addresses: minac@uwo.ca, reichst@math.ubc.ca

Submission: 2003, Sep 3

We study quadratic forms that can occur as trace forms $q_{L/K}$ of Galois field extensions $L/K$, under the assumption that $K$ contains a primitive $4$th root of unity. M. Epkenhans conjectured that $q_{L/K}$ is always 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.

2000 Mathematics Subject Classification:

Keywords and Phrases:

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