ON RAMIFIED TORSION POINTS ON A CURVE WITH STABLE REDUCTION OVER AN ABSOLUTELY UNRAMIFIED BASE

Hoshi, Yuichiro

doi:info:doi/10.18910/67013

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タイトル	ON RAMIFIED TORSION POINTS ON A CURVE WITH STABLE REDUCTION OVER AN ABSOLUTELY UNRAMIFIED BASE
著者	Hoshi, Yuichiro Hoshi, Yuichiro
抄録	Let p be an odd prime number, W an absolutely unramified p-adically complete discrete valuation ring with algebraically closed residue field, and X a curve of genus at least two over the field of fractions K of W. In the present paper, we study, under the assumption that X has stable reduction over W, torsion points on X, i.e., torsion points of the Jacobian variety J of X which lie on the image of the Albanese embedding X → J with respect to a K-rational point of X. A consequence of the main result of the present paper is that if, moreover, J has good reduction over W, then every torsion point on X is K-rational after multiplying p. This result is closely related to a conjecture of R. Coleman concerning the ramification of torsion points. For instance, this result leads us to a solution of the conjecture in the case where a given curve is hyperelliptic and of genus at least p.
公開者	Osaka University and Osaka City University, Departments of Mathematics
掲載誌名	Osaka Journal of Mathematics
巻	54
号	4
開始ページ	767
終了ページ	787
刊行年月	2017-10
ISSN	00306126
NCID	AA00765910
URL	http://hdl.handle.net/11094/67013
言語	英語
DOI	info:doi/10.18910/67013
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 54, Number 4 （2017-10）

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.54(4) P.767-P.787
DC.title	ON RAMIFIED TORSION POINTS ON A CURVE WITH STABLE REDUCTION OVER AN ABSOLUTELY UNRAMIFIED BASE
DC.creator	Hoshi, Yuichiro
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language" scheme="DCTERMS.RFC1766	英語
DCTERMS.issued" scheme="DCTERMS.W3CDTF	2017-10
DC.identifier" scheme="DCTERMS.URI	http://hdl.handle.net/11094/67013
DCTERMS.abstract	Let p be an odd prime number, W an absolutely unramified p-adically complete discrete valuation ring with algebraically closed residue field, and X a curve of genus at least two over the field of fractions K of W. In the present paper, we study, under the assumption that X has stable reduction over W, torsion points on X, i.e., torsion points of the Jacobian variety J of X which lie on the image of the Albanese embedding X → J with respect to a K-rational point of X. A consequence of the main result of the present paper is that if, moreover, J has good reduction over W, then every torsion point on X is K-rational after multiplying p. This result is closely related to a conjecture of R. Coleman concerning the ramification of torsion points. For instance, this result leads us to a solution of the conjecture in the case where a given curve is hyperelliptic and of genus at least p.
DC.identifier	info:doi/10.18910/67013
citation_title	ON RAMIFIED TORSION POINTS ON A CURVE WITH STABLE REDUCTION OVER AN ABSOLUTELY UNRAMIFIED BASE
citation_author	Hoshi, Yuichiro
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2017-10
citation_journal_title	Osaka Journal of Mathematics
citation_volume	54
citation_issue	4
citation_firstpage	767
citation_lastpage	787
citation_issn	00306126
citation_public_url	http://hdl.handle.net/11094/67013
citation_doi	info:doi/10.18910/67013

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