Construction of Zp-extensions with prescribed Iwasawa modules

Manabu Ozaki

doi:10.2969/jmsj/1191334086

Construction of Z_p-extensions with prescribed Iwasawa modules

Manabu Ozaki^*

^*Corresponding author for this work

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

10 Citations (Scopus)

Abstract

We construct Z_p-extensions whose Iwasawa modules have prescribed structure. Specifically, we give a Z_p-extension with prescribed finite Iwasawa module. Also we show that there exists a Z_p-extension with arbitrarily given Iwasawa μ-invariant. We apply the construction of such Z_p-extensions to a certain capitulation problem.

Original language	English
Pages (from-to)	787-801
Number of pages	15
Journal	Journal of the Mathematical Society of Japan
Volume	56
Issue number	3
DOIs	https://doi.org/10.2969/jmsj/1191334086
Publication status	Published - 2004
Externally published	Yes

Keywords

Iwasawa invariant
Iwasawa module
capitulation of ideals

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.2969/jmsj/1191334086

Cite this

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title = "Construction of Zp-extensions with prescribed Iwasawa modules",

abstract = "We construct Zp-extensions whose Iwasawa modules have prescribed structure. Specifically, we give a Zp-extension with prescribed finite Iwasawa module. Also we show that there exists a Zp-extension with arbitrarily given Iwasawa μ-invariant. We apply the construction of such Zp-extensions to a certain capitulation problem.",

keywords = "Iwasawa invariant, Iwasawa module, capitulation of ideals",

author = "Manabu Ozaki",

year = "2004",

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language = "English",

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AU - Ozaki, Manabu

PY - 2004

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AB - We construct Zp-extensions whose Iwasawa modules have prescribed structure. Specifically, we give a Zp-extension with prescribed finite Iwasawa module. Also we show that there exists a Zp-extension with arbitrarily given Iwasawa μ-invariant. We apply the construction of such Zp-extensions to a certain capitulation problem.

KW - Iwasawa invariant

KW - Iwasawa module

KW - capitulation of ideals

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M3 - Article

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JF - Journal of the Mathematical Society of Japan

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