There are genus one curves of every index over every number field

Simple item page
dc.creatorClark, Pete L.
dc.date2004-11-18
dc.date.accessioned2026-07-07T05:14:28Z
dc.date.available2026-07-07T05:14:28Z
dc.descriptionWe show that there exist genus one curves of every index over the rational numbers, answering affirmatively a question of Lang and Tate. The proof is "elementary" in the sense that it does not assume the finiteness of any Shafarevich-Tate group. On the other hand, using Kolyvagin's construction of a rational elliptic curve whose Mordell-Weil and Shafarevich-Tate groups are both trivial, we show that there are infinitely many curves of every index over every number field.
dc.description5 pages
dc.identifierhttps://arxiv.org/abs/math/0411413
dc.identifierhttp://arxiv.org/abs/math/0411413
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73286
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.titleThere are genus one curves of every index over every number field
dc.typetext

Files

Collections

arXiv