Title : Trace forms of Galois field extensions in the presence of roots of unity Abstract : 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. Dong Seung Kang BK21 Post-doc Position Seoul National University