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

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article

7 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 1

ASJC Scopus subject areas

Algebra and Number Theory

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Ozaki, M. (1997). On the cyclotomic unit group and the ideal class group of a real abelian number field. Journal of Number Theory, 64(2), 211-222. https://doi.org/10.1006/jnth.1997.2086

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