On tame pro-p Galois groups over basic ℤp-extensions

Yasushi Mizusawa, Manabu Ozaki

    Research output: Contribution to journalArticle

    7 Citations (Scopus)

    Abstract

    For a prime number p and a finite set S of prime numbers congruent to 1 modulo p, we consider the Galois group of the maximal pro-p-extension unramified outside S over the ℤp-extension of the rational number field. In this paper, we give a family of S for which the Galois group is a metacyclic pro-p group with an application to Greenberg's conjecture.

    Original languageEnglish
    Pages (from-to)1161-1173
    Number of pages13
    JournalMathematische Zeitschrift
    Volume273
    Issue number3-4
    DOIs
    Publication statusPublished - 2013 Apr

    Fingerprint

    Pro-p Groups
    Galois group
    Prime number
    Metacyclic Group
    Congruent
    Number field
    Modulo
    Finite Set
    Family

    Keywords

    • Greenberg's conjecture
    • Iwasawa theory
    • Tamely ramification

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    On tame pro-p Galois groups over basic ℤp-extensions. / Mizusawa, Yasushi; Ozaki, Manabu.

    In: Mathematische Zeitschrift, Vol. 273, No. 3-4, 04.2013, p. 1161-1173.

    Research output: Contribution to journalArticle

    Mizusawa, Yasushi ; Ozaki, Manabu. / On tame pro-p Galois groups over basic ℤp-extensions. In: Mathematische Zeitschrift. 2013 ; Vol. 273, No. 3-4. pp. 1161-1173.
    @article{c294f16ebb654946b5bb933a077eaf79,
    title = "On tame pro-p Galois groups over basic ℤp-extensions",
    abstract = "For a prime number p and a finite set S of prime numbers congruent to 1 modulo p, we consider the Galois group of the maximal pro-p-extension unramified outside S over the ℤp-extension of the rational number field. In this paper, we give a family of S for which the Galois group is a metacyclic pro-p group with an application to Greenberg's conjecture.",
    keywords = "Greenberg's conjecture, Iwasawa theory, Tamely ramification",
    author = "Yasushi Mizusawa and Manabu Ozaki",
    year = "2013",
    month = "4",
    doi = "10.1007/s00209-012-1048-2",
    language = "English",
    volume = "273",
    pages = "1161--1173",
    journal = "Mathematische Zeitschrift",
    issn = "0025-5874",
    publisher = "Springer New York",
    number = "3-4",

    }

    TY - JOUR

    T1 - On tame pro-p Galois groups over basic ℤp-extensions

    AU - Mizusawa, Yasushi

    AU - Ozaki, Manabu

    PY - 2013/4

    Y1 - 2013/4

    N2 - For a prime number p and a finite set S of prime numbers congruent to 1 modulo p, we consider the Galois group of the maximal pro-p-extension unramified outside S over the ℤp-extension of the rational number field. In this paper, we give a family of S for which the Galois group is a metacyclic pro-p group with an application to Greenberg's conjecture.

    AB - For a prime number p and a finite set S of prime numbers congruent to 1 modulo p, we consider the Galois group of the maximal pro-p-extension unramified outside S over the ℤp-extension of the rational number field. In this paper, we give a family of S for which the Galois group is a metacyclic pro-p group with an application to Greenberg's conjecture.

    KW - Greenberg's conjecture

    KW - Iwasawa theory

    KW - Tamely ramification

    UR - http://www.scopus.com/inward/record.url?scp=84874945540&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84874945540&partnerID=8YFLogxK

    U2 - 10.1007/s00209-012-1048-2

    DO - 10.1007/s00209-012-1048-2

    M3 - Article

    AN - SCOPUS:84874945540

    VL - 273

    SP - 1161

    EP - 1173

    JO - Mathematische Zeitschrift

    JF - Mathematische Zeitschrift

    SN - 0025-5874

    IS - 3-4

    ER -