Ordinary elliptic curves of high rank over $\bar F_p(x)$ with constant j-invariant II
| dc.creator | Diem, Claus | |
| dc.creator | Scholten, Jasper | |
| dc.date | 2005-09-26 | |
| dc.date | 2006-07-18 | |
| dc.date.accessioned | 2026-07-07T06:43:07Z | |
| dc.date.available | 2026-07-07T06:43:07Z | |
| dc.description | We show that for all odd primes $p$, there exist ordinary elliptic curves over $\bar{\mathbb{F}}_p(x)$ with arbitrarily high rank and constant $j$-invariant. This shows in particular that there are elliptic curves with arbitrarily high rank over these fields for which the corresponding elliptic surface is not supersingular. The result follows from a theorem which states that for all odd prime numbers $p$ and $\ell$, there exists a hyperelliptic curve over $\bar{\mathbb{F}}_p$ of genus $(\ell-1)/2$ whose Jacobian is isogenous to the power of one ordinary elliptic curve. | |
| dc.description | 14 pages, new version | |
| dc.identifier | https://arxiv.org/abs/math/0509600 | |
| dc.identifier | http://arxiv.org/abs/math/0509600 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102295 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G05; 11G20; 14H40; 14H52 | |
| dc.title | Ordinary elliptic curves of high rank over $\bar F_p(x)$ with constant j-invariant II | |
| dc.type | text |