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자연과학대학
수학전공
Journal papers
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The finitude of tamely ramified pro-p extensions of number fields with cyclic p-class groups
Title
The finitude of tamely ramified pro-p extensions of number fields with cyclic p-class groups
Authors
Lee
;
Yoonjin
;
Lim
;
Donghyeok
Ewha Authors
이윤진
SCOPUS Author ID
이윤진
Issue Date
2024
Journal Title
Journal of Number Theory
ISSN
0022-314X
Citation
Journal of Number Theory vol. 259, pp. 338 - 356
Keywords
Powerful pro-p groups
;
Ray class field tower
;
Tame Fontaine-Mazur conjecture
Publisher
Academic Press Inc.
Indexed
SCIE; SCOPUS
Document Type
Article
Abstract
Let p be an odd prime and F be a number field whose p-class group is cyclic. Let F{q} be the maximal pro-p extension of F which is unramified outside a single non-p-adic prime ideal q of F. In this work, we study the finitude of the Galois group G{q}(F) of F{q} over F. We prove that G{q}(F) is finite for the majority of q's such that the generator rank of G{q}(F) is two, provided that for p=3, F is not a complex quartic field containing the primitive third roots of unity. © 2024 Elsevier Inc.
DOI
10.1016/j.jnt.2024.01.005
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