Ordinary elliptic curves of high rank over $\bar F_p(x)$ with constant j-invariant

dc.creatorBouw, Irene I.
dc.creatorDiem, Claus
dc.creatorScholten, Jasper
dc.date2003-05-04
dc.date.accessioned2026-07-07T04:57:45Z
dc.date.available2026-07-07T04:57:45Z
dc.descriptionWe show that under the assumption of Artin's Primitive Root Conjecture, for all primes p there exist ordinary elliptic curves over $\bar F_p(x)$ with arbitrary high rank and constant j-invariant. For odd primes p, this result follows from a theorem which states that whenever p is a generator of (Z/ell Z)^*/<-1> (ell an odd prime) there exists a hyperelliptic curve over $\bar F_p$ whose Jacobian is isogenous to a power of one ordinary elliptic curve.
dc.description15 pages, 0 figures, LaTeX
dc.identifierhttps://arxiv.org/abs/math/0305064
dc.identifierhttp://arxiv.org/abs/math/0305064
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/67366
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subject11G05 (Primary); 11G20; 14H40; 14H52 (Secondary)
dc.titleOrdinary elliptic curves of high rank over $\bar F_p(x)$ with constant j-invariant
dc.typetext

Files

Collections