On the Arithmetic determination of the trace

2013/08/09 by Guillermo Mantilla-Soler, Mantilla-Soler, Guillermo
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1308.2187

This is an updated, and basically final version of this paper. A version of it is published in the Journal of Algebra

arxiv created 2015/10/17 · arxiv updated 2015/10/20

Abstract

Let K be a number field, which is tame and non totally real. In this article we give a numerical criterion, depending only on the ramification behavior of ramified primes in K, to decide whether or not the integral trace of K is isometric to the integral trace of another number field L. As a byproduct of our proofs here, and in contrast with our previous results for cubic fields of positive discriminant, we show that for cubic fields of negative discriminant isometry between integral traces is equivalent to equality of discriminants.

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