Geodesic
The integral trace form as a complete invariant for real $S_n$ number fields
Documenta mathematica, Tome 27 (2022), pp. 1865-1889.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

In this paper we show that the integral trace is a complete invariant for degree $n, S_n$ real number fields that satisfy certain ramification bound. Among the fields that our results cover, there are those of square free different ideal; for such fields we find an explicit description of the isometry group of the integral trace.
Classification : 11R80, 11R29, 11R21
Keywords: integral trace form, tame fields, \(S_n\)-extensions 
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     author = {Mantilla-Soler, Guillermo and Rivera, Carlos},
     title = {The integral trace form as a complete invariant for real {\(S_n\)} number fields},
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Mantilla-Soler, Guillermo; Rivera, Carlos. The integral trace form as a complete invariant for real \(S_n\) number fields. Documenta mathematica, Tome 27 (2022), pp. 1865-1889. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a19/