Notes on the structure of the ideal class groups of abelian number fields

Abstract

In this paper, we give explicit formulae of certain higher annihilators of the ideal class groups defined by V. Kolyvagin and K. Rubin, which come from Euler systems of Stickelberger elements and cyclotomic units. Further, using these explicit formulae, we reformulate Kolyvagin-Rubin's structure theorem of the ideal class groups of abelian number fields.