ON TAMELY RAMIFIED IWASAWA MODULES FOR THE CYCLOTOMIC Z_p-EXTENSION OF ABELIAN FIELDS

Itoh, Tsuyoshi

doi:info:doi/10.18910/29204

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タイトル	ON TAMELY RAMIFIED IWASAWA MODULES FOR THE CYCLOTOMIC Z_p-EXTENSION OF ABELIAN FIELDS
著者	Itoh, Tsuyoshi Itoh, Tsuyoshi
抄録	Let p be an odd prime, and k_∞ the cyclotomic Z_p-extension of an abelian field k. For a finite set S of rational primes which does not include p, we will consider the maximal S-ramified abelian pro-p extension M_S(k_∞) over k_∞. We shall give a formula of the Z_p-rank of Gal(M_S(k_∞)/k_∞). In the proof of this formula, we also show that M_<{q}>(k_∞)/L(k_∞) is a finite extension for every real abelian field k and every rational prime q distinct from p, where L(k_∞) is the maximal unramified abelian pro-p extension over k_∞.
公開者	Osaka University and Osaka City University, Departments of Mathematics
掲載誌名	Osaka Journal of Mathematics
巻	51
号	2
開始ページ	513
終了ページ	536
刊行年月	2014-04
ISSN	00306126
NCID	AA00765910
URL	http://hdl.handle.net/11094/29204
言語	英語
DOI	info:doi/10.18910/29204
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 51, Number 2　(2014-4）

著者版フラグ	publisher
NII資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
dcmi資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics.51(2) P.513-P.536
DC.title	ON TAMELY RAMIFIED IWASAWA MODULES FOR THE CYCLOTOMIC Z_p-EXTENSION OF ABELIAN FIELDS
DC.creator	Itoh, Tsuyoshi
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language" scheme="DCTERMS.RFC1766	英語
DCTERMS.issued" scheme="DCTERMS.W3CDTF	2014-04
DC.identifier" scheme="DCTERMS.URI	http://hdl.handle.net/11094/29204
DCTERMS.abstract	Let p be an odd prime, and k_∞ the cyclotomic Z_p-extension of an abelian field k. For a finite set S of rational primes which does not include p, we will consider the maximal S-ramified abelian pro-p extension M_S(k_∞) over k_∞. We shall give a formula of the Z_p-rank of Gal(M_S(k_∞)/k_∞). In the proof of this formula, we also show that M_<{q}>(k_∞)/L(k_∞) is a finite extension for every real abelian field k and every rational prime q distinct from p, where L(k_∞) is the maximal unramified abelian pro-p extension over k_∞.
DC.identifier	info:doi/10.18910/29204
citation_title	ON TAMELY RAMIFIED IWASAWA MODULES FOR THE CYCLOTOMIC Z_p-EXTENSION OF ABELIAN FIELDS
citation_author	Itoh, Tsuyoshi
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2014-04
citation_journal_title	Osaka Journal of Mathematics
citation_volume	51
citation_issue	2
citation_firstpage	513
citation_lastpage	536
citation_issn	00306126
citation_public_url	http://hdl.handle.net/11094/29204
citation_doi	info:doi/10.18910/29204

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