The circular units and the Stickelberger ideal of a cyclotomic field revisited

Radan Kučera¹

¹ Department of Mathematics and Statistics Faculty of Science Masaryk University Kotlářská 2 611 37 Brno, Czech Republic

Acta Arithmetica, Tome 174 (2016) no. 3, pp. 217-238

Résumé

The aim of this paper is a new construction of bases of the group of circular units and of the Stickelberger ideal for a family of abelian fields containing all cyclotomic fields, namely for any compositum of imaginary abelian fields, each ramified only at one prime. In contrast to the previous papers on this topic our approach consists in an explicit construction of Ennola relations. This gives an explicit description of the torsion parts of odd and even universal ordinary distributions, but it also allows us to give a shorter proof that the given set of elements is a basis. Moreover we obtain a presentation of the group of circular numbers for any field in the above mentioned family.

Détail

DOI : 10.4064/aa8009-4-2016

Keywords: paper construction bases group circular units stickelberger ideal family abelian fields containing cyclotomic fields namely compositum imaginary abelian fields each ramified only prime contrast previous papers topic approach consists explicit construction ennola relations gives explicit description torsion parts odd even universal ordinary distributions allows shorter proof given set elements basis moreover obtain presentation group circular numbers field above mentioned family