Ranks of rational points of the Jacobian varieties of hyperelliptic curves

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dc.contributor.authorIm, Bo-Haeko
dc.contributor.authorKim, Byoung Duko
dc.date.accessioned2018-11-22T07:06:04Z-
dc.date.available2018-11-22T07:06:04Z-
dc.date.created2018-11-19-
dc.date.created2018-11-19-
dc.date.created2018-11-19-
dc.date.created2018-11-19-
dc.date.issued2019-02-
dc.identifier.citationJOURNAL OF NUMBER THEORY, v.195, pp.23 - 50-
dc.identifier.issn0022-314X-
dc.identifier.urihttp://hdl.handle.net/10203/246871-
dc.description.abstractIn this paper, we obtain bounds for the Mordell Weil ranks over certain Z(p)-extensions (including cyclotomic Z(p)-extensions) of a wide range of abelian varieties defined over a number field F whose primes above p are totally ramified over F/Q. We assume that the abelian varieties may have good non-ordinary reduction at primes above p. Our work is a generalization of [5], in which the second author generalized Perrin-Riou's Iwasawa theory for elliptic curves over Q with supersingular reduction ([14]) to elliptic curves defined over the above-mentioned number field F. As a result, we obtain bounds of the Mordell Weil ranks over cyclotomic extensions of the Jacobian varieties of y(2) = x(3pN) + ax(pN) + b and y(2pM) = X-3pN + ax(pN) + b. (C) 2018 Elsevier Inc. All rights reserved.-
dc.languageEnglish-
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE-
dc.titleRanks of rational points of the Jacobian varieties of hyperelliptic curves-
dc.typeArticle-
dc.identifier.wosid000449038500002-
dc.identifier.scopusid2-s2.0-85054125555-
dc.type.rimsART-
dc.citation.volume195-
dc.citation.beginningpage23-
dc.citation.endingpage50-
dc.citation.publicationnameJOURNAL OF NUMBER THEORY-
dc.identifier.doi10.1016/j.jnt.2018.08.002-
dc.contributor.localauthorIm, Bo-Hae-
dc.contributor.nonIdAuthorKim, Byoung Du-
dc.description.isOpenAccessN-
dc.type.journalArticleArticle-
dc.subject.keywordAuthorAbelian variety-
dc.subject.keywordAuthorJacobian variety-
dc.subject.keywordAuthorSelmer group-
dc.subject.keywordAuthorMordell-Weil group-
dc.subject.keywordAuthorIwasawa theory-
dc.subject.keywordPlusIWASAWA-THEORY-
dc.subject.keywordPlusELLIPTIC-CURVES-
dc.subject.keywordPlusSUPERSINGULAR PRIMES-
dc.subject.keywordPlusABELIAN-VARIETIES-
dc.subject.keywordPlusMAPS-
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