Helfgott, Harald Andrés

[["dc.bibliographiccitation.firstpage","684"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","Advances in Mathematics"],["dc.bibliographiccitation.lastpage","731"],["dc.bibliographiccitation.volume","198"],["dc.contributor.author","Conrad, B."],["dc.contributor.author","Conrad, K."],["dc.contributor.author","Helfgott, H."],["dc.date.accessioned","2017-09-07T11:47:53Z"],["dc.date.available","2017-09-07T11:47:53Z"],["dc.date.issued","2005"],["dc.description.abstract","For a global field K and an elliptic curve over , Silverman's specialization theorem implies for all but finitely many . If this inequality is strict for all but finitely many t, the elliptic curve is said to have elevated rank. All known examples of elevated rank for rest on the parity conjecture for elliptic curves over , and the examples are all isotrivial. Some additional standard conjectures over imply that there does not exist a non-isotrivial elliptic curve over with elevated rank. In positive characteristic, an analogue of one of these additional conjectures is false. Inspired by this, for the rational function field over any finite field with characteristic , we construct an explicit 2-parameter family of non-isotrivial elliptic curves over (depending on arbitrary ) such that, under the parity conjecture, each has elevated rank."],["dc.identifier.doi","10.1016/j.aim.2005.06.013"],["dc.identifier.gro","3146789"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4591"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0001-8708"],["dc.subject","Elliptic curve Root number Function fields"],["dc.title","Root numbers and ranks in positive characteristic"],["dc.type","journal_article"],["dc.type.internalPublication","no"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]