On the fibres of an elliptic surface where the rank does not jump

Simple item page
dc.catalogadorpau
dc.contributor.authorCaro Reyes, Jerson
dc.contributor.authorPastén Vásquez, Héctor
dc.date.accessioned2023-07-13T19:48:12Z
dc.date.available2023-07-13T19:48:12Z
dc.date.issued2022
dc.description.abstractFor a nonconstant elliptic surface over P1 defined over Q , it is a result of Silverman [‘Heights and the specialization map for families of abelian varieties’, J. reine angew. Math. 342 (1983), 197–211] that the Mordell–Weil rank of the fibres is at least the rank of the group of sections, up to finitely many fibres. If the elliptic surface is nonisotrivial, one expects that this bound is an equality for infinitely many fibres, although no example is known unconditionally. Under the Bunyakovsky conjecture, such an example has been constructed by Neumann [‘Elliptische Kurven mit vorgeschriebenem Reduktionsverhalten. I’, Math. Nachr. 49 (1971), 107–123] and Setzer [‘Elliptic curves of prime conductor’, J. Lond. Math. Soc. (2) 10 (1975), 367–378]. In this note, we show that the Legendre elliptic surface has the desired property, conditional on the existence of infinitely many Mersenne primes.
dc.fechaingreso.objetodigital2023-07-12
dc.format.extent7 páginas
dc.fuente.origenCambridge University Press
dc.identifier.doi10.1017/S0004972722001368
dc.identifier.issn0004-9727
dc.identifier.urihttps://doi.org/10.1017/S0004972722001368
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/74172
dc.information.autorucFacultad de Matemáticas; Caro Reyes, Jerson; 0000-0001-8547-3365 ; 1092696
dc.information.autorucFacultad de Matemáticas; Pastén Vásquez, Héctor; 0000-0002-7789-8459; 1080628
dc.language.isoen
dc.nota.accesoContenido completo
dc.revistaBulletin of the Australian Mathematical Society
dc.rightsacceso abierto
dc.rights.licenseAttribution 4.0 International (CC BY 4.0)
dc.rights.urihttp://creativecommons.org/licenses/by/4.0)
dc.subjectElliptic surface
dc.subjectRank
dc.subjectParity conjecture
dc.subject.ddc510
dc.subject.deweyMatemática física y químicaes_ES
dc.titleOn the fibres of an elliptic surface where the rank does not jumpes_ES
dc.typeartículo
sipa.codpersvinculados1092696
sipa.codpersvinculados1080628
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
on-the-fibres-of-an-elliptic-surface-where-the-rank-does-not-jump.pdf
Size:
245.31 KB
Format:
Adobe Portable Document Format
Description:
Download
Collections
Artículos de revistas