Mod-p reducibility, the torsion subgroup, and the Shafarevich-Tate group
| dc.creator | Agashe, Amod | |
| dc.date | 2009-05-26 | |
| dc.date.accessioned | 2026-07-07T13:18:15Z | |
| dc.date.available | 2026-07-07T13:18:15Z | |
| dc.description | Let $E$ be an optimal elliptic curve over $\Q$ of prime conductor $N$. We show that if for an odd prime $p$, the mod $p$ representation associated to $E$ is reducible (in particular, if $p$ divides the order of the torsion subgroup of $E(\Q)$), then the $p$-primary component of the Shafarevich-Tate group of $E$ is trivial. We also state a related result for more general abelian subvarieties of $J_0(N)$ and mention what to expect if $N$ is not prime. | |
| dc.identifier | https://arxiv.org/abs/0905.4217 | |
| dc.identifier | http://arxiv.org/abs/0905.4217 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/231371 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G05; 11G10; 11G18; 11G40; 14G | |
| dc.title | Mod-p reducibility, the torsion subgroup, and the Shafarevich-Tate group | |
| dc.type | text |