Guillermo MantillaAffiliation: University of Wisconsin Email: mantilla@math.wisc.edu Title Of Talk: Integral trace forms associated to cubic extensions Abstract: Given a nonzero integer $d$ we know, by Hermite's Theorem, that there exist only finitely many cubic number fields of discriminant $d$. A natural question is, how to refine the discriminant in such way that we can tell, when two of these fields are isomorphic. Here we consider the binary quadratic form $q_K: Tr_{K/ \mathbb{Q}}(x^2)|_{O^{0}_{K}}$, and we show that if $d$ is a positive fundamental discriminant, then the isomorphism class of $q_K$, as a quadratic form over $\mathbb{Z}^{2}$, gives such a refinement.
Last update made Tue Jan 20 22:37:28 EST 2009.
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