The integral trace form as a complete invariant for real S_n number fields

2018/12/07 by Guillermo Mantilla-Soler, Mantilla-Soler, Guillermo, Carlos Mallén Rivera +1
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1812.03133

openalex publication_date 2018/12/07 · openalex created_date 2022/08/01 · openalex updated_date 2026/07/28

Abstract

In the past the first named author has studied to what extent the integral trace can characterize a number field beyond what the discriminant does. The cases of cyclic number fields and non-totally real fields are more or less settled, concluding that for such fields the integral trace does not always characterize the field. In this paper we show that the integral trace is a complete invariant for degree n, S_n real number number fields that satisfy certain ramification bound. Among the real S_n fields that our results cover, there are those of square free different ideal. Moreover, for such fields we find an explicit description of the isometry group of the integral trace.

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