NL repository
menu
검색
Library
Browse
Communities & Collections
By Date
Authors
Titles
Subject
My Repository
My Account
Receive email updates
Edit Profile
DSpace at EWHA
자연과학대학
수학전공
Journal papers
View : 505 Download: 0
Infinite families of cyclotomic function fields with any prescribed class group rank
Title
Infinite families of cyclotomic function fields with any prescribed class group rank
Authors
Yoo J.
;
Lee Y.
Ewha Authors
이윤진
SCOPUS Author ID
이윤진
Issue Date
2021
Journal Title
Journal of Pure and Applied Algebra
ISSN
0022-4049
Citation
Journal of Pure and Applied Algebra vol. 225, no. 9
Keywords
Class group rank
;
Cyclotomic function field
;
Ideal class group
;
Kummer extension
;
Maximal real subfield
Publisher
Elsevier B.V.
Indexed
SCIE; SCOPUS
Document Type
Article
Abstract
We prove the existence of the maximal real subfields of cyclotomic extensions over the rational function field k=Fq(T) whose class groups can have arbitrarily large ℓn-rank, where Fq is the finite field of prime power order q. We prove this in a constructive way: we explicitly construct infinite families of the maximal real subfields k(Λ)+ of cyclotomic function fields k(Λ) whose ideal class groups have arbitrary ℓn-rank for n = 1, 2, and 3, where ℓ is a prime divisor of q−1. We also obtain a tower of cyclotomic function fields Ki whose maximal real subfields have ideal class groups of ℓn-ranks getting increased as the number of the finite places of k which are ramified in Ki get increased for i≥1. Our main idea is to use the Kummer extensions over k which are subfields of k(Λ)+, where the infinite prime ∞ of k splits completely. In fact, we construct the maximal real subfields k(Λ)+ of cyclotomic function fields whose class groups contain the class groups of our Kummer extensions over k. We demonstrate our results by presenting some examples calculated by MAGMA at the end. © 2020 Elsevier B.V.
DOI
10.1016/j.jpaa.2020.106658
Appears in Collections:
자연과학대학
>
수학전공
>
Journal papers
Files in This Item:
There are no files associated with this item.
Export
RIS (EndNote)
XLS (Excel)
XML
Show full item record
Find@EWHA
트윗하기
BROWSE
Communities & Collections
By Date
Authors
Titles
Subject