On the ℤp-ranks of tamely ramified Iwasawa modules

Tsuyoshi Itoh, Yasushi Mizusawa, Manabu Ozaki

    Research output: Contribution to journalArticle

    8 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

    Fingerprint

    P-rank
    Number field
    Module
    Linear independence
    Imaginary Quadratic Field
    Cyclotomic
    Algebraic number
    Galois group
    Prime number
    P-adic
    Logarithm
    Finite Set
    Explicit Formula
    Theorem

    Keywords

    • ℤ-extension
    • Iwasawa module
    • tame ramification

    ASJC Scopus subject areas

    • Algebra and Number Theory

    Cite this

    On the ℤp-ranks of tamely ramified Iwasawa modules. / Itoh, Tsuyoshi; Mizusawa, Yasushi; Ozaki, Manabu.

    In: International Journal of Number Theory, Vol. 9, No. 6, 09.2013, p. 1491-1503.

    Research output: Contribution to journalArticle

    Itoh, Tsuyoshi ; Mizusawa, Yasushi ; Ozaki, Manabu. / On the ℤp-ranks of tamely ramified Iwasawa modules. In: International Journal of Number Theory. 2013 ; Vol. 9, No. 6. pp. 1491-1503.
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