Intersecting the torsion of elliptic curves

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dc.catalogadorjca
dc.contributor.authorGarcía-Fritz, Natalia
dc.contributor.authorPasten, Hector
dc.date.accessioned2024-04-23T20:11:08Z
dc.date.available2024-04-23T20:11:08Z
dc.date.issued2023
dc.description.abstractBogomolov and Tschinkel [‘Algebraic varieties over small fields’, Diophantine Geometry, U. Zannier (ed.), CRM Series, 4 (Scuola Normale Superiore di Pisa, Pisa, 2007), 73–91] proved that, given two complex elliptic curves E1 and E2 along with even degree-2 maps πj: Ej → P1 having different branch loci, the intersection of the image of the torsion points of E1 and E2 under their respective πj is finite. They conjectured (also in works with Fu) that the cardinality of this intersection is uniformly bounded independently of the elliptic curves. The recent proof of the uniform Manin–Mumford conjecture implies a full solution of the Bogomolov–Fu–Tschinkel conjecture. In this paper, we prove a generalisation of the Bogomolov–Fu–Tschinkel conjecture whereby, instead of even degree-2 maps, one can use any rational functions of bounded degree on the elliptic curves as long as they have different branch loci. Our approach combines Nevanlinna theory with the uniform Manin–Mumford conjecture. With similar techniques, we also prove a result on lower bounds for ranks of elliptic curves over number fields.
dc.fechaingreso.objetodigital2024-09-11
dc.fuente.origenCambridge University Press
dc.identifier.doi10.1017/S000497272300134X
dc.identifier.issn0004-9727
dc.identifier.urihttps://doi.org/10.1017/S000497272300134X
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/85305
dc.information.autorucFacultad de Matemáticas;García Fritz, Natalia;S/I;1060092
dc.information.autorucFacultad de Matemáticas;Pasten Vásquez, Hector;0000-0002-7789-8459;1080628
dc.language.isoen
dc.nota.accesocontenido parcial
dc.pagina.final8
dc.pagina.inicio1
dc.revistaBulletin of the Australian Mathematical Society
dc.rightsacceso restringido
dc.subjectElliptic curve
dc.subjectTorsion
dc.subjectRank
dc.subjectMordell–Lang
dc.subjectManin–Mumford
dc.subjectUniformity
dc.subject.ddc510
dc.subject.deweyMatemática física y químicaes_ES
dc.titleIntersecting the torsion of elliptic curves
dc.typeartículo
sipa.codpersvinculados1060092
sipa.codpersvinculados1080628
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