Rank gain of Jacobian varieties over finite Galois extensions

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dc.contributor.authorIm, Bo-Haeko
dc.contributor.authorWallace, Erikko
dc.date.accessioned2018-01-22T02:03:48Z-
dc.date.available2018-01-22T02:03:48Z-
dc.date.created2017-11-25-
dc.date.created2017-11-25-
dc.date.created2017-11-25-
dc.date.issued2018-03-
dc.identifier.citationJOURNAL OF NUMBER THEORY, v.184, pp.68 - 84-
dc.identifier.issn0022-314X-
dc.identifier.urihttp://hdl.handle.net/10203/237144-
dc.description.abstractLet K be a number field, and let X -> P-K(1) be a degree p covering branched only at 0, 1, and infinity. If K is a field containing a primitive p-th root of unity then the covering of P-1 is Galois over K, and if p is congruent to 1 mod 6, then there is an automorphism sigma of X which cyclically permutes the branch points. Under these assumptions, we show that the Jacobian of both X and X/<sigma > gain rank over infinitely many linearly disjoint cyclic degree p-extensions of K. We also show the existence of an infinite family of elliptic curves whose j-invariants are parametrized by a modular function on Gamma(0)(3) and that gain rank over infinitely many cyclic degree 3-extensions of Q.-
dc.languageEnglish-
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE-
dc.titleRank gain of Jacobian varieties over finite Galois extensions-
dc.typeArticle-
dc.identifier.wosid000416612800003-
dc.identifier.scopusid2-s2.0-85030478946-
dc.type.rimsART-
dc.citation.volume184-
dc.citation.beginningpage68-
dc.citation.endingpage84-
dc.citation.publicationnameJOURNAL OF NUMBER THEORY-
dc.identifier.doi10.1016/j.jnt.2017.08.010-
dc.contributor.localauthorIm, Bo-Hae-
dc.contributor.nonIdAuthorWallace, Erik-
dc.description.isOpenAccessN-
dc.type.journalArticleArticle-
dc.subject.keywordAuthorJacobian varieties-
dc.subject.keywordAuthorElliptic curves-
dc.subject.keywordAuthorRank-
dc.subject.keywordPlusCURVES-
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