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

• Autorzy: Radan Kučera
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11R18: Cyclotomic extensions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 174
• Numer: 3
• Strony: 217-238

Daty

wydano

2016

Twórcy

autor

Radan Kučera

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

Identyfikatory

DOI

10.4064/aa8009-4-2016