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

Yasushi Mizusawa; Manabu Ozaki

doi:10.1007/s00209-012-1048-2

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

Yasushi Mizusawa^*, Manabu Ozaki

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

8 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 ℤ_p-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 language	English
Pages (from-to)	1161-1173
Number of pages	13
Journal	Mathematische Zeitschrift
Volume	273
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-012-1048-2
Publication status	Published - 2013 Apr

Keywords

Greenberg's conjecture
Iwasawa theory
Tamely ramification

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/s00209-012-1048-2

Cite this

@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 = apr,

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

SN - 0025-5874

VL - 273

SP - 1161

EP - 1173

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3-4

ER -