Journal of the Mathematical Society of Japan

Construction of Zp-extensions with prescribed Iwasawa modules

Manabu OZAKI

Full-text: Open access

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.

Article information

Source
J. Math. Soc. Japan, Volume 56, Number 3 (2004), 787-801.

Dates
First available in Project Euclid: 2 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1191334086

Digital Object Identifier
doi:10.2969/jmsj/1191334086

Mathematical Reviews number (MathSciNet)
MR2071673

Zentralblatt MATH identifier
1142.11368

Subjects
Primary: 11R23: Iwasawa theory
Secondary: 11R29: Class numbers, class groups, discriminants

Keywords
Iwasawa module Iwasawa invariant capitulation of ideals

Citation

OZAKI, Manabu. Construction of $Z_{p}$ -extensions with prescribed Iwasawa modules. J. Math. Soc. Japan 56 (2004), no. 3, 787--801. doi:10.2969/jmsj/1191334086. https://projecteuclid.org/euclid.jmsj/1191334086


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