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

Manabu Ozaki

doi:10.1006/jnth.1997.2086

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

Manabu Ozaki^*

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

LetKbe a real abelian number field satisfying certain conditions andK_nthenth layer of the cyclotomic Z_p-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 ofK_n. Supposing that Greenberg's conjecture is valid, we shall show that these two groups are isomorphic as Galois modules for sufficiently largen.

Original language	English
Pages (from-to)	211-222
Number of pages	12
Journal	Journal of Number Theory
Volume	64
Issue number	2
DOIs	https://doi.org/10.1006/jnth.1997.2086
Publication status	Published - 1997 Jun

ASJC Scopus subject areas

Algebra and Number Theory

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Cite this

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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.",

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

Abstract

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