Construction of Zp-extensions with prescribed Iwasawa modules

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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.

Original languageEnglish
Pages (from-to)787-801
Number of pages15
JournalJournal of the Mathematical Society of Japan
Volume56
Issue number3
DOIs
Publication statusPublished - 2004 Jan 1

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Keywords

  • Iwasawa invariant
  • Iwasawa module
  • capitulation of ideals

ASJC Scopus subject areas

  • Mathematics(all)

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