Trace forms of Galois field extensions in the presence of roots of unity

D.-S. Kang and Zinovy Reichstein

Let $L/K$ be a Galois field extension and let $G_2$ be a Sylow subgroup of Gal$(L/K)$. We show that if $G_2$ is not abelian then the trace form of $L/K$ is hyperbolic, provided that $K$ contains certain roots of unity.