On the cyclotomic unit group and the ideal class group of a real abelian number field

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Abstract

LetKbe a real abelian number field satisfying certain conditions andKnthenth layer of the cyclotomic Zp-extension ofK. We study the relations between thep-Sylow subgroup of the ideal class group and that of the unit group modulo the cyclotomic unit group ofKn. Supposing that Greenberg's conjecture is valid, we shall show that these two groups are isomorphic as Galois modules for sufficiently largen.

Original languageEnglish
Pages (from-to)211-222
Number of pages12
JournalJournal of Number Theory
Volume64
Issue number2
DOIs
Publication statusPublished - 1997 Jun 1

ASJC Scopus subject areas

  • Algebra and Number Theory

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