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Ideal Class Groups of Iwasawa-Theoretical Abelian Extensions Over the Rational Field

Ideal Class Groups of Iwasawa-Theoretical Abelian Extensions Over the Rational Field Throughout this paper, we shall suppose that all algebraic number fields, namely, all algebraic extensions over the rational field Q, are contained in the complex field C. Let P be the set of all prime numbers. For any algebraic number field F , let C F denote the ideal class group of F and, writing F + for the maximal real subfield of F , let denote the kernel of the norm map from C F to the ideal class group of F + ; for each l ∈ P , let C F ( l ) denote the l -class group of F , that is, the l -primary component of C F , and let denote the l -primary component of . Furthermore, for each l ∈ P , we denote by Z l the ring of l -adic integers. © The London Mathematical Society « Previous | Next Article » Table of Contents This Article J. London Math. Soc. (2002) 66 (2): 257-275. doi: 10.1112/S0024610702003502 » Abstract Free Full Text (PDF) Free Classifications Notes and Papers Services Article metrics Alert me when cited Alert me if corrected Find similar articles Similar articles in Web of Science Add to my archive Download citation Citing Articles Load citing article information Citing articles via CrossRef Citing articles via Scopus Citing articles via Web of Science Citing articles via Google Scholar Google Scholar Articles by Horie, K. Search for related content Related Content Load related web page information Share Email this article CiteULike Delicious Facebook Google+ Mendeley Twitter What's this? Search this journal: Advanced » Current Issue October 2015 92 (2) Alert me to new issues The Journal About the journal Rights & Permissions We are mobile – find out more Published on behalf of London Mathematical Society Impact Factor: 0.820 5-Yr impact factor: 0.925 Editors Anthony J. Scholl Ivan Smith View full editorial board LMS journals now available in full MathJax HTML. MathJax is an open-source JavaScript display engine that produces high-quality mathematics in all modern browsers. To learn more about MathJax, please visit their site at www.MathJax.org. For Authors Instructions to authors Including copyright assignment, and offprints order forms. Alerting Services Email table of contents Email Advance Access CiteTrack XML RSS feed Corporate Services What we offer Advertising sales Reprints Supplements var taxonomies = ("SCI01470"); Most Most Read Categorical Representations of Endomorphism Near-Rings Proximal Analysis and Approximate Subdifferentials Embedding Theorems for Groups On Certain Sets of Integers A Simple Proof of a Theorem of Erdos and Szekeres » View all Most Read articles Most Cited Using random sets as oracles Exponential Sums Equations and the Schanuel Conjecture Regularity Theorems and Heat Kernel for Elliptic Operators The l2-Cohomology of Artin Groups Estimates for the Number of Sums and Products and for Exponential Sums in Fields of Prime Order » View all Most Cited articles Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department. Online ISSN 1469-7750 - Print ISSN 0024-6107 Copyright © 2015 London Mathematical Society Oxford Journals Oxford University Press Site Map Privacy Policy Cookie Policy Legal Notices Frequently Asked Questions Other Oxford University Press sites: Oxford University Press Oxford Journals China Oxford Journals Japan Academic & Professional books Children's & Schools Books Dictionaries & Reference Dictionary of National Biography Digital Reference English Language Teaching Higher Education Textbooks International Education Unit Law Medicine Music Online Products & Publishing Oxford Bibliographies Online Oxford Dictionaries Online Oxford English Dictionary Oxford Language Dictionaries Online Oxford Scholarship Online Reference Rights and Permissions Resources for Retailers & Wholesalers Resources for the Healthcare Industry Very Short Introductions World's Classics var gaJsHost = (("https:" == document.location.protocol) ? "https://ssl." : "http://www."); document.write(unescape("%3Cscript src='" + gaJsHost + "google-analytics.com/ga.js' type='text/javascript'%3E%3C/script%3E")); try { var pageTracker = _gat._getTracker("UA-189672-16"); pageTracker._setDomainName(".oxfordjournals.org"); pageTracker._trackPageview(); } catch(err) {} http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the London Mathematical Society Oxford University Press

Ideal Class Groups of Iwasawa-Theoretical Abelian Extensions Over the Rational Field

Ideal Class Groups of Iwasawa-Theoretical Abelian Extensions Over the Rational Field

Journal of the London Mathematical Society , Volume 66 (2) – Oct 1, 2002

Abstract

Throughout this paper, we shall suppose that all algebraic number fields, namely, all algebraic extensions over the rational field Q, are contained in the complex field C. Let P be the set of all prime numbers. For any algebraic number field F , let C F denote the ideal class group of F and, writing F + for the maximal real subfield of F , let denote the kernel of the norm map from C F to the ideal class group of F + ; for each l ∈ P , let C F ( l ) denote the l -class group of F , that is, the l -primary component of C F , and let denote the l -primary component of . Furthermore, for each l ∈ P , we denote by Z l the ring of l -adic integers. © The London Mathematical Society « Previous | Next Article » Table of Contents This Article J. London Math. Soc. (2002) 66 (2): 257-275. doi: 10.1112/S0024610702003502 » Abstract Free Full Text (PDF) Free Classifications Notes and Papers Services Article metrics Alert me when cited Alert me if corrected Find similar articles Similar articles in Web of Science Add to my archive Download citation Citing Articles Load citing article information Citing articles via CrossRef Citing articles via Scopus Citing articles via Web of Science Citing articles via Google Scholar Google Scholar Articles by Horie, K. Search for related content Related Content Load related web page information Share Email this article CiteULike Delicious Facebook Google+ Mendeley Twitter What's this? Search this journal: Advanced » Current Issue October 2015 92 (2) Alert me to new issues The Journal About the journal Rights & Permissions We are mobile – find out more Published on behalf of London Mathematical Society Impact Factor: 0.820 5-Yr impact factor: 0.925 Editors Anthony J. Scholl Ivan Smith View full editorial board LMS journals now available in full MathJax HTML. MathJax is an open-source JavaScript display engine that produces high-quality mathematics in all modern browsers. To learn more about MathJax, please visit their site at www.MathJax.org. For Authors Instructions to authors Including copyright assignment, and offprints order forms. Alerting Services Email table of contents Email Advance Access CiteTrack XML RSS feed Corporate Services What we offer Advertising sales Reprints Supplements var taxonomies = ("SCI01470"); Most Most Read Categorical Representations of Endomorphism Near-Rings Proximal Analysis and Approximate Subdifferentials Embedding Theorems for Groups On Certain Sets of Integers A Simple Proof of a Theorem of Erdos and Szekeres » View all Most Read articles Most Cited Using random sets as oracles Exponential Sums Equations and the Schanuel Conjecture Regularity Theorems and Heat Kernel for Elliptic Operators The l2-Cohomology of Artin Groups Estimates for the Number of Sums and Products and for Exponential Sums in Fields of Prime Order » View all Most Cited articles Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department. Online ISSN 1469-7750 - Print ISSN 0024-6107 Copyright © 2015 London Mathematical Society Oxford Journals Oxford University Press Site Map Privacy Policy Cookie Policy Legal Notices Frequently Asked Questions Other Oxford University Press sites: Oxford University Press Oxford Journals China Oxford Journals Japan Academic & Professional books Children's & Schools Books Dictionaries & Reference Dictionary of National Biography Digital Reference English Language Teaching Higher Education Textbooks International Education Unit Law Medicine Music Online Products & Publishing Oxford Bibliographies Online Oxford Dictionaries Online Oxford English Dictionary Oxford Language Dictionaries Online Oxford Scholarship Online Reference Rights and Permissions Resources for Retailers & Wholesalers Resources for the Healthcare Industry Very Short Introductions World's Classics var gaJsHost = (("https:" == document.location.protocol) ? "https://ssl." : "http://www."); document.write(unescape("%3Cscript src='" + gaJsHost + "google-analytics.com/ga.js' type='text/javascript'%3E%3C/script%3E")); try { var pageTracker = _gat._getTracker("UA-189672-16"); pageTracker._setDomainName(".oxfordjournals.org"); pageTracker._trackPageview(); } catch(err) {}

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References (16)

Publisher
Oxford University Press
Copyright
Copyright © 2015 London Mathematical Society
ISSN
0024-6107
eISSN
1469-7750
DOI
10.1112/S0024610702003502
Publisher site
See Article on Publisher Site

Abstract

Throughout this paper, we shall suppose that all algebraic number fields, namely, all algebraic extensions over the rational field Q, are contained in the complex field C. Let P be the set of all prime numbers. For any algebraic number field F , let C F denote the ideal class group of F and, writing F + for the maximal real subfield of F , let denote the kernel of the norm map from C F to the ideal class group of F + ; for each l ∈ P , let C F ( l ) denote the l -class group of F , that is, the l -primary component of C F , and let denote the l -primary component of . Furthermore, for each l ∈ P , we denote by Z l the ring of l -adic integers. © The London Mathematical Society « Previous | Next Article » Table of Contents This Article J. London Math. Soc. (2002) 66 (2): 257-275. doi: 10.1112/S0024610702003502 » Abstract Free Full Text (PDF) Free Classifications Notes and Papers Services Article metrics Alert me when cited Alert me if corrected Find similar articles Similar articles in Web of Science Add to my archive Download citation Citing Articles Load citing article information Citing articles via CrossRef Citing articles via Scopus Citing articles via Web of Science Citing articles via Google Scholar Google Scholar Articles by Horie, K. Search for related content Related Content Load related web page information Share Email this article CiteULike Delicious Facebook Google+ Mendeley Twitter What's this? Search this journal: Advanced » Current Issue October 2015 92 (2) Alert me to new issues The Journal About the journal Rights & Permissions We are mobile – find out more Published on behalf of London Mathematical Society Impact Factor: 0.820 5-Yr impact factor: 0.925 Editors Anthony J. Scholl Ivan Smith View full editorial board LMS journals now available in full MathJax HTML. MathJax is an open-source JavaScript display engine that produces high-quality mathematics in all modern browsers. To learn more about MathJax, please visit their site at www.MathJax.org. For Authors Instructions to authors Including copyright assignment, and offprints order forms. Alerting Services Email table of contents Email Advance Access CiteTrack XML RSS feed Corporate Services What we offer Advertising sales Reprints Supplements var taxonomies = ("SCI01470"); Most Most Read Categorical Representations of Endomorphism Near-Rings Proximal Analysis and Approximate Subdifferentials Embedding Theorems for Groups On Certain Sets of Integers A Simple Proof of a Theorem of Erdos and Szekeres » View all Most Read articles Most Cited Using random sets as oracles Exponential Sums Equations and the Schanuel Conjecture Regularity Theorems and Heat Kernel for Elliptic Operators The l2-Cohomology of Artin Groups Estimates for the Number of Sums and Products and for Exponential Sums in Fields of Prime Order » View all Most Cited articles Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department. Online ISSN 1469-7750 - Print ISSN 0024-6107 Copyright © 2015 London Mathematical Society Oxford Journals Oxford University Press Site Map Privacy Policy Cookie Policy Legal Notices Frequently Asked Questions Other Oxford University Press sites: Oxford University Press Oxford Journals China Oxford Journals Japan Academic & Professional books Children's & Schools Books Dictionaries & Reference Dictionary of National Biography Digital Reference English Language Teaching Higher Education Textbooks International Education Unit Law Medicine Music Online Products & Publishing Oxford Bibliographies Online Oxford Dictionaries Online Oxford English Dictionary Oxford Language Dictionaries Online Oxford Scholarship Online Reference Rights and Permissions Resources for Retailers & Wholesalers Resources for the Healthcare Industry Very Short Introductions World's Classics var gaJsHost = (("https:" == document.location.protocol) ? "https://ssl." : "http://www."); document.write(unescape("%3Cscript src='" + gaJsHost + "google-analytics.com/ga.js' type='text/javascript'%3E%3C/script%3E")); try { var pageTracker = _gat._getTracker("UA-189672-16"); pageTracker._setDomainName(".oxfordjournals.org"); pageTracker._trackPageview(); } catch(err) {}

Journal

Journal of the London Mathematical SocietyOxford University Press

Published: Oct 1, 2002

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