On the ℤp-ranks of tamely ramified Iwasawa modules

Tsuyoshi Itoh, Yasushi Mizusawa, Manabu Ozaki

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

For a finite set S of prime numbers, we consider the S-ramified Iwasawa module which is the Galois group of the maximal abelian pro-p-extension unramified outside S over the cyclotomic ℤp-extension of a number field k. In the case where S does not contain p and k is the rational number field or an imaginary quadratic field, we give the explicit formulae of the ℤp-ranks of the S-ramified Iwasawa modules by using Brumer's p-adic version of Baker's theorem on the linear independence of logarithms of algebraic numbers.

Original languageEnglish
Pages (from-to)1491-1503
Number of pages13
JournalInternational Journal of Number Theory
Volume9
Issue number6
DOIs
Publication statusPublished - 2013 Sep 1

Keywords

  • Iwasawa module
  • tame ramification
  • ℤ-extension

ASJC Scopus subject areas

  • Algebra and Number Theory

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